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Journey to the Edge of Reason: The Life of Kurt Gödel
A New York Times Critics' Top Book of 2021 • A Booklist Top Ten Biography of 2021 • A Kirkus Reviews Best Science Book of 2021The first major biography written for a general audience of the logician and mathematician whose Incompleteness Theorems helped launch a modern scientific revolution.
Nearly a hundred years after its publication, Kurt Gödel’s famous proof that every mathematical system must contain propositions that are true—yet never provable—continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.
Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of the Institute for Advanced Study in Princeton, NJ, where Gödel and Einstein both worked.
Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.
Nearly a hundred years after its publication, Kurt Gödel’s famous proof that every mathematical system must contain propositions that are true—yet never provable—continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.
Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of the Institute for Advanced Study in Princeton, NJ, where Gödel and Einstein both worked.
Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.
368 pages, Kindle Edition
Published May 11, 2021
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About the author
Stephen Budiansky
25 books113 followersHistorian and journalist Stephen Budiansky is the author of twelve books about military history, science, and nature.
His latest book is The Bloody Shirt: Terror After Appomattox, which chronicles the struggles of five courageous men in the post-Civil War South as they battled a rising tide of terrorist violence aimed at usurping the newly won rights of the freedmen.
His latest book is The Bloody Shirt: Terror After Appomattox, which chronicles the struggles of five courageous men in the post-Civil War South as they battled a rising tide of terrorist violence aimed at usurping the newly won rights of the freedmen.
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December 8, 2021
The Word Made Flesh in Vienna
It was Alan Turing who discovered an important implication of Kurt Gōdel’s Incompleteness Proof. One of the consequences of the impossibility of finding a justification for the logic of arithmetic is that some mathematical propositions, although true, cannot be shown to be so. The logical steps required to prove their veracity are infinite. In technical terms, this makes them undecidable. That is, both the proposition and its negation are possible without contradiction - a mathematical incongruity that stops reason dead in its tracks.
It strikes me that the central irony of Gödel’s life as described by Budiansky is precisely this kind of undecidability applied to himself. Gödel had incredible insight and ability in logical reasoning. But for him reason was a syntactical process, that is, a purely symbolic exercise. It had nothing to do with the world outside mathematics. Its semantics, that is the connection of abstract logic to the world outside of mathematics, was something Gödel had no interest in, and very little ability.
Gödel was not unaware of his handicap. In notes to himself quoted by Budiansky, he makes it clear that he is often simply incapable of what Immanuel Kant called Practical Reason, the logic of right action: “… [I]t takes me five to ten times as long to reach a decision than other people.” Budiansky reports that he filled page after page with procedures to employ in making decisions. But his self-diagnoses transformed routinely into self-fulfilling prophecies. It is as if his inner demon of abstraction and procedural inference had been given the task of correcting itself. The result was predictably not very encouraging. Yet he obsessively continued the practice of self-analysis and self-correction throughout his life, trying, it seems, to prove the reflexive paradox of his own Proof wrong.
His decisiveness and fluency in mathematics were entirely absent from his personal and social life. Taking action frequently made him ill with uncertainty. For example, leaving Vienna to take up a position at The Institute of Advanced Studies in Princeton, he became so distressed he had to return to Vienna. After his year long stay in America, he hospitalised himself almost immediately upon arrival home with concern about the prudence of his return. Then venturing again the following year to Princeton for his second stint at the Institute, he resigned almost immediately claiming stress and ill health. He had decided to return to an increasingly violent Austria in which university life had all but been destroyed! Subsequently when it was clear that Austrian fascism had annihilated the intellectual life of the country and the Anschluss by Hitler was only days away, Gödel was offered an appointment at the University of Notre Dame. Yet he dithered interminably and finally inexplicably rejected the offer. Neither sensible judgement nor fortitude were Gödel’s forté.
This profound indecisiveness was apparently accompanied by an equally profound fear of being observed, that is of being seen as a person apart from his mathematical accomplishments. He did give occasional lectures in front of colleagues and otherwise sympathetic audiences. But at his courses at Princeton, Gödel stood speaking with his back to the students facing the blackboard but never writing on it. Clearly he wanted his students attention solely on the ‘mask’ of his symbolic reasoning and not directed to his physical person. Yet his stance suggests not shyness or even a sense of threat but almost shame for betraying the guilty secret of mathematics as well as his own judgment in devoting his life to a ‘defective’ pursuit of truth.
So as an example of someone who identifies him or herself as their work, Gödel is hard to better. What seems especially significant though is that his quasi-paranoia was directed at himself rather than at those he perceived as observing him. This doesn’t appear to have been a form of autism - Gödel did frequently, and annoyingly, ignore events he found distracting but he could be charming and had a droll sense of humour. He was apparently a devoted and sensitive friend. It was his own physicality that Gödel did not trust, perhaps originating in his recognition that he was unable to make reliable decisions outside of mathematics, particularly about his own life. That he had discovered the black hole in mathematical reasoning could well have been as much as a psychic tragedy as much as a professional triumph.
This is obviously a terrible psychological burden to bear. It is a commonplace that mathematicians do their best work in their youth. Gödel berated himself in his mature years for his lack of work of the same quality that had made his reputation. No assurances from friends, colleagues or university administrators that he was still regarded as an important mathematician could convince him to mitigate his own self-reflective judgement. He simply could not be consoled. And as his German-speaking colleagues, especially Einstein, either died or left Princeton, Gödel showed full-blown signs of breakdown.
Another implication of Gödel’s Proof was developed by his friend Alfred Tarski. It turns out that not only are some propositions undecidable but also that even the notion of what constitutes truth is undefinable in arithmetic. Could this be the subconscious origin of Gödel’s indecisiveness and defensiveness? Certainly many others have lived out their neuroses in useful ways.
Perhaps Gödel’s life, therefore, was not only an example of total devotion to mathematics but also a physical manifestation of his primitive insight about it. He fought passionately against metaphysics using patently metaphysical arguments, arguing for example that his Proof showed both the Platonic reality of numbers and that this reality was permanently beyond human comprehension. As he matured is it possible the basic incongruity in his Self of abstract reason simply took its course to disintegration? That he became more himself in other words. I’m not being trite when I suggest that Gödel had a bug in his organic operating system, a genetic quirk that led him gradually into extreme self-alienation.
So for me the question this biography raises is something both personal to Gödel and yet general to the science of mind. Is it better, that is to say more accurate, more productive and in some ways more fair, to describe Gödel as a psychologically aberrant personality, or as someone who just lived out his fate as best he could? In more poetic terms Gödel seems very much the incarnation of his own mathematical word, a person of total although tragic integrity.
Might it be that each of us has some similarly in-built genetic logic that will have its way in whatever circumstances we might find ourselves, in fact motivating us to create those circumstances as well as respond to them?
It was Alan Turing who discovered an important implication of Kurt Gōdel’s Incompleteness Proof. One of the consequences of the impossibility of finding a justification for the logic of arithmetic is that some mathematical propositions, although true, cannot be shown to be so. The logical steps required to prove their veracity are infinite. In technical terms, this makes them undecidable. That is, both the proposition and its negation are possible without contradiction - a mathematical incongruity that stops reason dead in its tracks.
It strikes me that the central irony of Gödel’s life as described by Budiansky is precisely this kind of undecidability applied to himself. Gödel had incredible insight and ability in logical reasoning. But for him reason was a syntactical process, that is, a purely symbolic exercise. It had nothing to do with the world outside mathematics. Its semantics, that is the connection of abstract logic to the world outside of mathematics, was something Gödel had no interest in, and very little ability.
Gödel was not unaware of his handicap. In notes to himself quoted by Budiansky, he makes it clear that he is often simply incapable of what Immanuel Kant called Practical Reason, the logic of right action: “… [I]t takes me five to ten times as long to reach a decision than other people.” Budiansky reports that he filled page after page with procedures to employ in making decisions. But his self-diagnoses transformed routinely into self-fulfilling prophecies. It is as if his inner demon of abstraction and procedural inference had been given the task of correcting itself. The result was predictably not very encouraging. Yet he obsessively continued the practice of self-analysis and self-correction throughout his life, trying, it seems, to prove the reflexive paradox of his own Proof wrong.
His decisiveness and fluency in mathematics were entirely absent from his personal and social life. Taking action frequently made him ill with uncertainty. For example, leaving Vienna to take up a position at The Institute of Advanced Studies in Princeton, he became so distressed he had to return to Vienna. After his year long stay in America, he hospitalised himself almost immediately upon arrival home with concern about the prudence of his return. Then venturing again the following year to Princeton for his second stint at the Institute, he resigned almost immediately claiming stress and ill health. He had decided to return to an increasingly violent Austria in which university life had all but been destroyed! Subsequently when it was clear that Austrian fascism had annihilated the intellectual life of the country and the Anschluss by Hitler was only days away, Gödel was offered an appointment at the University of Notre Dame. Yet he dithered interminably and finally inexplicably rejected the offer. Neither sensible judgement nor fortitude were Gödel’s forté.
This profound indecisiveness was apparently accompanied by an equally profound fear of being observed, that is of being seen as a person apart from his mathematical accomplishments. He did give occasional lectures in front of colleagues and otherwise sympathetic audiences. But at his courses at Princeton, Gödel stood speaking with his back to the students facing the blackboard but never writing on it. Clearly he wanted his students attention solely on the ‘mask’ of his symbolic reasoning and not directed to his physical person. Yet his stance suggests not shyness or even a sense of threat but almost shame for betraying the guilty secret of mathematics as well as his own judgment in devoting his life to a ‘defective’ pursuit of truth.
So as an example of someone who identifies him or herself as their work, Gödel is hard to better. What seems especially significant though is that his quasi-paranoia was directed at himself rather than at those he perceived as observing him. This doesn’t appear to have been a form of autism - Gödel did frequently, and annoyingly, ignore events he found distracting but he could be charming and had a droll sense of humour. He was apparently a devoted and sensitive friend. It was his own physicality that Gödel did not trust, perhaps originating in his recognition that he was unable to make reliable decisions outside of mathematics, particularly about his own life. That he had discovered the black hole in mathematical reasoning could well have been as much as a psychic tragedy as much as a professional triumph.
This is obviously a terrible psychological burden to bear. It is a commonplace that mathematicians do their best work in their youth. Gödel berated himself in his mature years for his lack of work of the same quality that had made his reputation. No assurances from friends, colleagues or university administrators that he was still regarded as an important mathematician could convince him to mitigate his own self-reflective judgement. He simply could not be consoled. And as his German-speaking colleagues, especially Einstein, either died or left Princeton, Gödel showed full-blown signs of breakdown.
Another implication of Gödel’s Proof was developed by his friend Alfred Tarski. It turns out that not only are some propositions undecidable but also that even the notion of what constitutes truth is undefinable in arithmetic. Could this be the subconscious origin of Gödel’s indecisiveness and defensiveness? Certainly many others have lived out their neuroses in useful ways.
Perhaps Gödel’s life, therefore, was not only an example of total devotion to mathematics but also a physical manifestation of his primitive insight about it. He fought passionately against metaphysics using patently metaphysical arguments, arguing for example that his Proof showed both the Platonic reality of numbers and that this reality was permanently beyond human comprehension. As he matured is it possible the basic incongruity in his Self of abstract reason simply took its course to disintegration? That he became more himself in other words. I’m not being trite when I suggest that Gödel had a bug in his organic operating system, a genetic quirk that led him gradually into extreme self-alienation.
So for me the question this biography raises is something both personal to Gödel and yet general to the science of mind. Is it better, that is to say more accurate, more productive and in some ways more fair, to describe Gödel as a psychologically aberrant personality, or as someone who just lived out his fate as best he could? In more poetic terms Gödel seems very much the incarnation of his own mathematical word, a person of total although tragic integrity.
Might it be that each of us has some similarly in-built genetic logic that will have its way in whatever circumstances we might find ourselves, in fact motivating us to create those circumstances as well as respond to them?
June 3, 2021
Compared with the sciences, mathematics can seem relatively short on interesting characters. There's no doubt that the subject of Stephen Budiansky's biography - Kurt Gödel was an engaging subject, from his effective shattering of the certainties of the mathematical system to his increasing oddity in his later life, but perhaps surprisingly this claims to be the first significant biography of Gödel.
Budiansky gives us plenty on the context of Gödel's work and life - and a brief exploration of Gödel's incompleteness theorems (though their nature means that it's hard to give more than a faint impression of how they do what they do). Unfortunately, though, this is not a particularly accessible biography.
With many scientific/mathematical biographies, poor accessibility can be down to a lack of context, with too much focus on the detailed complexities of the science or the maths. Here, though, the issue is the reverse. There is far too much context, so much so that Gödel often gets lost amongst all the detail. After a few introductory pages giving a flash forward to Gödel's death, the first real chapter illustrates this all too well - there is so much material focussing on Austria as it was when Gödel was born that we don’t meet the young Gödel until page 41.
Similarly, later on, the book can feel more like a biography of, say, the disputed genius (or oddball) philosopher Wittgenstein as it is of Gödel. I don't know if it's just that there isn't too much biographical detail on Gödel himself (which would explain why it has taken so long to get a biography), or if Budiansky simply enjoys going off on tangents, but I found it hard not to keep skipping forward to find the next mention of the purported subject of the book.
A bit of a frustrating experience, then. There is no doubt that there is plenty of interesting material here, but far too much history, philosophical context and detail on obscure academics that Gödel interacted with, and not enough on the man himself.
Budiansky gives us plenty on the context of Gödel's work and life - and a brief exploration of Gödel's incompleteness theorems (though their nature means that it's hard to give more than a faint impression of how they do what they do). Unfortunately, though, this is not a particularly accessible biography.
With many scientific/mathematical biographies, poor accessibility can be down to a lack of context, with too much focus on the detailed complexities of the science or the maths. Here, though, the issue is the reverse. There is far too much context, so much so that Gödel often gets lost amongst all the detail. After a few introductory pages giving a flash forward to Gödel's death, the first real chapter illustrates this all too well - there is so much material focussing on Austria as it was when Gödel was born that we don’t meet the young Gödel until page 41.
Similarly, later on, the book can feel more like a biography of, say, the disputed genius (or oddball) philosopher Wittgenstein as it is of Gödel. I don't know if it's just that there isn't too much biographical detail on Gödel himself (which would explain why it has taken so long to get a biography), or if Budiansky simply enjoys going off on tangents, but I found it hard not to keep skipping forward to find the next mention of the purported subject of the book.
A bit of a frustrating experience, then. There is no doubt that there is plenty of interesting material here, but far too much history, philosophical context and detail on obscure academics that Gödel interacted with, and not enough on the man himself.
Read
December 11, 2025I often struggle how to review non-fiction books I read as i end up with a summary, or rarely a polemic. The former is not valuable and the latter is not always helpful. This I am afraid is not an exception. So I will focus here on just two and half things that I’ve taken from this biography. Also many words would be just the author’s words quoted.
1. Vienna between the wars. How quick Nazism become widely popular in spite of Vienna was a cultural capital of central Europe.
Before the Great War, Vienna was the capital of big sprouting and multicultural Austro-Hungarian empire. After the war it has become the capital of a smallish state. However, it seems that a few features of that society both positive and negative have survived that first war.
First and for most, the level of general education and fascination with culture and science was extremely high:
Therefore it is not surprising that this environment produced and cultivated quite a few geniuses (John von Neumann, Godel, Wittgentstein but also Popper, Hayek, Polanyi and the writers Musil, Roth, Broch plus of course grandpa Freud to name just a few). They have influenced the world for at least the rest of the century.
However, this has combined with a very 'turbulent' politics. Even before the WW1 the freedom of press was high. However the level of police surveillance was very high as well: ‘While they are grumbling they are content,” remarked Franz I, whose secret police compiled a dossier for him on every single one of his subjects. “It’s only when they fall silent that they are dangerous.’
Since the wave of liberalisation giving Jewish populations the rights in the mid of the 19th century, the level of antisemitism has become legitimate political issue: Appealing primarily to the Catholic lower middle classes who felt most threatened by the economic and social ascendance of the Jews, the Christian–Social party enjoyed a meteoric rise in the 1890s with their discovery that fanning the flames of anti-Jewish resentment could also be the one great unifier in polyglot Austria.
I dare say that the situation is not dissimilar to the current strong resentment of immigration in the West when some of the immigrants are scapegoated by the politicians for legitimate economic concerns of the disadvantaged. And a lot of limited resources are directed to inflame this hatred and not very successful fight with the inflow of people rather than improving social and economic condition for everyone.
We all know how extreme was the polarisation of society in Austria and Germany at that time. I also knew of the suppression of communists in Germany and earlier fights between the right and the left paramilitaries. Earlier this year, i’ve read Elias Cannetti’s memoirs where he talked about July 1927 resurrection in Vienna. The protesters have started the fire in the Palace of Justice, but then this was brutally surpassed by the shooting of alive rounds killing a hundred at least. It has made a life long impression on him and raised his interest in the behaviour of crowds. He ended up winning a Noble. But i did not know that the radical left was still going relatively strong until mid-thirties in Austria. And the conflict escalated for the last time in February 1934 resulted in much bigger killings:
In the course of three days of clashes, government forces used light artillery to shell the Karl-Marx-Hof, one of the large communal housing projects that were the most prominent emblems of Red Vienna. More than a thousand members of the Schutzbund and other civilians were killed.
The story of sliding into Nazism is more familiar. What still is quite shocking to me how popular that movement was and how quick the membership has grown to millions. The government attempted to ban the party but it did not help: outlawing of the Nazi Party made barely a dent in the giddy enthusiasm for Germany’s Führer among students and faculty at the University of Vienna.
The German Students’ Union began drawing up blacklists of “undesirable” professors and handing out leaflets warning fellow students not to attend their lectures. This has reminded me of overreaching by woke movement in some elite institutions of higher education.
Hahn, Schlick, and their growing circle of protégés were, in Karl Sigmund’s concise description, a left-wing pocket in a right-wing university of a left-wing town in a right-wing country. Infamously, Professor Schlick has been murdered soon afterwards by a mentally unstable chap who was arrested, got through the trial but then i believe was released.
I do not know their reasons but it seems a shocking number. I do not believe all of them did it due to the risk of their lives. After the defeat of in WW2 the austrians went through denazification, however a bit half-heartedly it seems:
I am not sure what would be an ideal balance of this process of denazification. It is very hard to find an equilibrium between the coherence of society and justice. Considering the membership of the nazis was so widespread, i even not sure how sincere this denazification have been in Austria. Also i am not sure i would even think about it ten years ago. Only the political reality of nowadays makes me be sceptical about such issues. So that was an arc of how a very cultured, economically advanced society has become Nazi.
On a side note, when many of the austrian intellectuals have moved to America they were a bit bemused. As a bit of a comic relief, I cannot refrain but quote a quote in full from a letter sent my the one of them to his friend still in Europe:
And another wonderful anecdote:
2. Godel: “My theory is rationalistic, idealistic, optimistic, and theological”
Each time i read a biography i convince myself of unknowability of the other. But here is the paradox: it makes me want more biographies. Especially I am fascinated how creative people discover, create, think that process, think of themselves. I know that by definition there is an enigma there that cannot be properly understood. But approaching this enigma is by itself very intriguing.
Having read this book, I've learned a few more facts about Godel and his time. Not much else. I still do not know how a mind can come up with something like an incompleteness theorem being very idealistic but on a very rational grounds and being paranoid about day-to-day life. What i gathered though that Godel believed that that mathematical intuition (in the narrow sense - a feeling that a set of axioms is true) is akin to other types perceptions such as eyesight for example. Therefore he did not believe that mathematics is just language like any other (Wittgenstein’s view). He believed mathematics has a meaning by itself, not only language of science and exist independently of human mind. He also did not believe that a machine could be created that ‘literally duplicate the reasoning, learning, planning, and problem-solving ability of the human mind’ probably because his views on mathematical intuition as well as a coronary of his theorem. He was prone to severe paranoia.
The quotes expanding all of this in under
He emigrated in the US before the war and never set a foot on European continent after that. But he always maintained passionate correspondence with his mother. When she was becoming old and frail he has written her the letter. Look at the beauty of this mind:
We need his logic but more over we need his faith.
1. Vienna between the wars. How quick Nazism become widely popular in spite of Vienna was a cultural capital of central Europe.
Before the Great War, Vienna was the capital of big sprouting and multicultural Austro-Hungarian empire. After the war it has become the capital of a smallish state. However, it seems that a few features of that society both positive and negative have survived that first war.
First and for most, the level of general education and fascination with culture and science was extremely high:
When Albert Einstein came to town to give a public lecture on the Theory of Relativity in 1921, the organizers had to hastily change the planned venue from a six-hundred-seat lecture hall in the public education institute, the Urania, to the Großer Konzerthaus, the largest concert hall in the city, with a capacity of two thousand. Tickets sold out in two days. With extra seats and standing room, the actual size of the audience as reported in the newspapers approached three thousand.
Therefore it is not surprising that this environment produced and cultivated quite a few geniuses (John von Neumann, Godel, Wittgentstein but also Popper, Hayek, Polanyi and the writers Musil, Roth, Broch plus of course grandpa Freud to name just a few). They have influenced the world for at least the rest of the century.
However, this has combined with a very 'turbulent' politics. Even before the WW1 the freedom of press was high. However the level of police surveillance was very high as well: ‘While they are grumbling they are content,” remarked Franz I, whose secret police compiled a dossier for him on every single one of his subjects. “It’s only when they fall silent that they are dangerous.’
Since the wave of liberalisation giving Jewish populations the rights in the mid of the 19th century, the level of antisemitism has become legitimate political issue: Appealing primarily to the Catholic lower middle classes who felt most threatened by the economic and social ascendance of the Jews, the Christian–Social party enjoyed a meteoric rise in the 1890s with their discovery that fanning the flames of anti-Jewish resentment could also be the one great unifier in polyglot Austria.
When confronted with his own continuing and cordial business and social relations with a good number of Vienna’s prominent Jewish business leaders, Lueger (the long standing mayor of Vienna) responded with a famous bit of flippant, Viennese-accented double-think, Wer a Jud is, bestimm’ i’—“ I decide who is a Jew.” Lueger’s cynicism and hypocrisy in exploiting the ugliest lurking hatreds out of political expediency prompted one of those Jewish associates to rebuke him, “I am not blaming you for being anti-Semitic. I am blaming you for not being anti-Semitic
I dare say that the situation is not dissimilar to the current strong resentment of immigration in the West when some of the immigrants are scapegoated by the politicians for legitimate economic concerns of the disadvantaged. And a lot of limited resources are directed to inflame this hatred and not very successful fight with the inflow of people rather than improving social and economic condition for everyone.
We all know how extreme was the polarisation of society in Austria and Germany at that time. I also knew of the suppression of communists in Germany and earlier fights between the right and the left paramilitaries. Earlier this year, i’ve read Elias Cannetti’s memoirs where he talked about July 1927 resurrection in Vienna. The protesters have started the fire in the Palace of Justice, but then this was brutally surpassed by the shooting of alive rounds killing a hundred at least. It has made a life long impression on him and raised his interest in the behaviour of crowds. He ended up winning a Noble. But i did not know that the radical left was still going relatively strong until mid-thirties in Austria. And the conflict escalated for the last time in February 1934 resulted in much bigger killings:
In the course of three days of clashes, government forces used light artillery to shell the Karl-Marx-Hof, one of the large communal housing projects that were the most prominent emblems of Red Vienna. More than a thousand members of the Schutzbund and other civilians were killed.
The story of sliding into Nazism is more familiar. What still is quite shocking to me how popular that movement was and how quick the membership has grown to millions. The government attempted to ban the party but it did not help: outlawing of the Nazi Party made barely a dent in the giddy enthusiasm for Germany’s Führer among students and faculty at the University of Vienna.
The German Students’ Union began drawing up blacklists of “undesirable” professors and handing out leaflets warning fellow students not to attend their lectures. This has reminded me of overreaching by woke movement in some elite institutions of higher education.
Hahn, Schlick, and their growing circle of protégés were, in Karl Sigmund’s concise description, a left-wing pocket in a right-wing university of a left-wing town in a right-wing country. Infamously, Professor Schlick has been murdered soon afterwards by a mentally unstable chap who was arrested, got through the trial but then i believe was released.
“The Germans are first-class Nazis, but lousy anti-Semites,” someone observed. “The Austrians are lousy Nazis, but by God what first-class anti-Semites they are!” That first night, a mob broke into the Palais Ephrussi, swarmed up its grand staircase and smashed their way through the house, finally dragging a large ornate desk to the hallway and pitching it over the handrail onto the flagstones of the courtyard below.
So many Austrians rushed to take out memberships in the Nazi Party—the “March violets,” they were sarcastically called—that the authorities stopped accepting new applications. Adele dutifully sent in hers, along with the 2 Reichsmark fee, but was never enrolled. Her mother, Hildegarde Porkert, however, made it in time (membership No. 2,654,956, issued April 2, 1938).
I do not know their reasons but it seems a shocking number. I do not believe all of them did it due to the risk of their lives. After the defeat of in WW2 the austrians went through denazification, however a bit half-heartedly it seems:
After a brief and cursory period of denazification at the university, most of those responsible for the purges of Jews and liberals returned to the positions they had secured at the expense of their victims. Viktor Christian, the SS authority on the “Jewish Question” who had plundered Jewish libraries and graves, regained his university pension after a general amnesty by the government in 1950, and then was elected an honorary member of the Anthropological Society and, in 1960, honored with a Golden Doctorate from the University of Vienna. ...Within the Faculty of Philosophy, 77 percent of the professors were found to have been members of the Nazi Party, but two-thirds of those were able to regain academic positions in Austria within just a few years of the war’s end, half of them to the very same posts they had held at the University of Vienna during the Nazi.
I am not sure what would be an ideal balance of this process of denazification. It is very hard to find an equilibrium between the coherence of society and justice. Considering the membership of the nazis was so widespread, i even not sure how sincere this denazification have been in Austria. Also i am not sure i would even think about it ten years ago. Only the political reality of nowadays makes me be sceptical about such issues. So that was an arc of how a very cultured, economically advanced society has become Nazi.
On a side note, when many of the austrian intellectuals have moved to America they were a bit bemused. As a bit of a comic relief, I cannot refrain but quote a quote in full from a letter sent my the one of them to his friend still in Europe:
Overall, the internal connections of the faculty are stronger than ours; one sees each other at all kinds of meetings and also privately. One is allowed less intrigue and spitefulness than with us. You let your fellow man live and there is amazingly little personal intrigue. There is much socializing, but due to its superficiality terribly boring. We try to get through with a minimum, which is not at all easy: Maria is constantly visited by the professors’ wives; the rule demands that you reply to these visits, from which follow dinner invitations, soon one is inevitably forced into an endless chain of boredom. Luckily the men are not so terribly bad as the wives, who constantly get together in clubs and generally rule their lives as a kind of higher power. For a doctor of philosophy one must go to school for at least 20 years, but people at 30 years are perhaps as mature as our 18-year-olds. It is the immaturity and naiveté that makes the people so uninteresting, we think.… Our impression is that nervous and neurotic characters are almost completely absent here, at least nothing is outwardly shown. People are robust, healthy, self-assured, the women almost all pretty but not one beautiful, all dressed fashionably and well but not distinctively and not truly elegantly. It is not so much from a feeling of inferiority as from an aspiring childishness that Americans in all their actions and speech (discreetly but clearly) keep pointing out, “We can do that too, we also have culture.
And another wonderful anecdote:
Siegel’s unconventional living arrangement, a bachelor sharing a house with two female friends, had aroused the particular censure of the dean’s wife. As he disgustedly informed his fellow refugee Richard Courant, “It would be meaningless to escape the sadism of Göring’s only to get under the yoke of Mrs. Eisenhart’s notion of morality.… Please do not be offended that I do not like your America.
2. Godel: “My theory is rationalistic, idealistic, optimistic, and theological”
Each time i read a biography i convince myself of unknowability of the other. But here is the paradox: it makes me want more biographies. Especially I am fascinated how creative people discover, create, think that process, think of themselves. I know that by definition there is an enigma there that cannot be properly understood. But approaching this enigma is by itself very intriguing.
Having read this book, I've learned a few more facts about Godel and his time. Not much else. I still do not know how a mind can come up with something like an incompleteness theorem being very idealistic but on a very rational grounds and being paranoid about day-to-day life. What i gathered though that Godel believed that that mathematical intuition (in the narrow sense - a feeling that a set of axioms is true) is akin to other types perceptions such as eyesight for example. Therefore he did not believe that mathematics is just language like any other (Wittgenstein’s view). He believed mathematics has a meaning by itself, not only language of science and exist independently of human mind. He also did not believe that a machine could be created that ‘literally duplicate the reasoning, learning, planning, and problem-solving ability of the human mind’ probably because his views on mathematical intuition as well as a coronary of his theorem. He was prone to severe paranoia.
The quotes expanding all of this in under
He emigrated in the US before the war and never set a foot on European continent after that. But he always maintained passionate correspondence with his mother. When she was becoming old and frail he has written her the letter. Look at the beauty of this mind:
You pose in your last letter the momentous question, whether I believe we shall meet in the hereafter. About that I can only say the following: If the world is constructed rationally and has a meaning, then that must be so. For what kind of a sense would there be in bringing forth a creature (man), who has such a broad field of possibilities of his own development and of relationships, and then not allow him to achieve 1/1000 of it. That would be approximately as if someone laid the foundation for a house with much effort and expenditure of money, then let everything go to ruin again. Does one have a reason to assume that the world is set up rationally? I believe so. For it is certainly not chaotic and arbitrary, but rather, as science shows, the greatest regularity and order reign in everything.…So, it follows directly that our earthly existence, since it in and of itself has at most a very dubious meaning, can only be a means to an end for another existence.
We need his logic but more over we need his faith.
July 16, 2021
I did not get exposed to the wonders of higher mathematics at an age where it would have made any difference to me in how I chose to pursue my education. Given what I now know, I have few regrets about this. Still, I remember the pleasures shortly after college of working through a book by Douglas Hofstadter - “Godel, Escher, Bach: an Eternal Golden Braid”. I still remember the fun in seeing the links among mathematics, graphic art, and baroque counterpoint as intellectual achievements. Hofstadter’s book was for a long time the champion among long and widely discussed books that ended up not being read - or read very far. Today it is easier to construct the league tables on such a competition by checking on Kindle to see how far into a long book the comments extend. Piketty’s books are among today’s leaders.
The problem with Godel, Escher, Bach is that I do not recall it saying much about Godel’s life. Stephen Budiansky’s book addresses this gap and provides an engaging account of an unusual man. Godel came of age intellectually in interwar Austria. Judging from all of the people he networked with then, this was a tough intellectual neighborhood. He published the paper that established his fame in 1931 at the age of 25. He had other papers but from this first paper, Godel’s work influenced whole areas ol logic, mathematics and meta mathematics as well as related areas (computer science).
The 1930s proved a difficult decade, with the normal stresses and strains of getting established, coupled with the rise of the Nazis and their takeover of Austrian universities after 1938. Like many others, Godel fled Austria and came to the US, where he became established at Princeton and its Institute for Advanced Study. In times of troubles, it helps to be a world class genius - and also to have friends like Albert Einstein and John Von Neumann. Godel was well known for his daily walks with Einstein in Princeton. He spent the remainder of his life at Princeton, where he died in 1978.
It is reasonable to ask what sort of person accomplishes what Godel accomplished. This is a problem si biographies of genius - most readers do not qualify. Budiansky does a good job at telling the story and explaining what he can of the math and logic. The biography also shows that Godel was a highly eccentric individual whose peculiarities were well recognized by his colleagues. He would likely have received better treatment today, but that is hard to know. Princeton seemed to treat him well.
This is an accessible and readable biography that is well worth the effort if ones interest run this way.
The problem with Godel, Escher, Bach is that I do not recall it saying much about Godel’s life. Stephen Budiansky’s book addresses this gap and provides an engaging account of an unusual man. Godel came of age intellectually in interwar Austria. Judging from all of the people he networked with then, this was a tough intellectual neighborhood. He published the paper that established his fame in 1931 at the age of 25. He had other papers but from this first paper, Godel’s work influenced whole areas ol logic, mathematics and meta mathematics as well as related areas (computer science).
The 1930s proved a difficult decade, with the normal stresses and strains of getting established, coupled with the rise of the Nazis and their takeover of Austrian universities after 1938. Like many others, Godel fled Austria and came to the US, where he became established at Princeton and its Institute for Advanced Study. In times of troubles, it helps to be a world class genius - and also to have friends like Albert Einstein and John Von Neumann. Godel was well known for his daily walks with Einstein in Princeton. He spent the remainder of his life at Princeton, where he died in 1978.
It is reasonable to ask what sort of person accomplishes what Godel accomplished. This is a problem si biographies of genius - most readers do not qualify. Budiansky does a good job at telling the story and explaining what he can of the math and logic. The biography also shows that Godel was a highly eccentric individual whose peculiarities were well recognized by his colleagues. He would likely have received better treatment today, but that is hard to know. Princeton seemed to treat him well.
This is an accessible and readable biography that is well worth the effort if ones interest run this way.
January 2, 2025
Kurt Gödel ranks with the likes of Karl Friedrich Gauss and George Cantor as among the world’s greatest mathematicians. And now, he has a full biography, that sets him within the late Austro-Hungarian Monarchy, as a Sudenten German who later moved to Austria, and as a man plagued ever more by various forms of mental illness as he aged.
One of the funniest quotes is one that stands in stark contrast to the famous Douglas Hofstadter book, “Gödel, Escher, Bach.” That is: “Bach and Wagner make me nervous.”
Not so funny is that, while Hofstadter had plenty of biographical elements about Bach, he had almost none about Escher and none on Gödel. This book remedies that in spades.
Gödel is best known for his Incompleteness Theorem, but on the math and philosophy side, had more than that, and “informed” discussions of relativity and more in physics.
Gödel had other oddities besides comment about Bach and Wagner. He was a diehard mathematical Platonist, but others exist today. That said, he seems to have been something like a diehard Platonist period.
That’s enough to give a good taste of this book, but without getting too deep into spoiler alert territory. Even clicking open the spoiler alert won't give all away.
That said, there are a couple of errata and issues in the book.
One minor one is that Budiansky claims Wiener schnitzel is really nothing more than cotoletta alla Milanese imported from Italy in the 1850s, allegedly by Radetsky. In 2007, a linguist totally debunked this.
The larger issue is one of omission. Many ideas that many people attribute to Gödel’s Incompleteness Theorem actually come from Tarski’s Undefinability Theorem. Tarski’s theorem extends beyond mathematics into semantics in general. That said, Budiansky isn’t alone. Realistically, Hofstadter should have written “Tarski, Escher, Bach.” That said, in turn, Gödel did apparently discover this first, but never published, so the technical credit goes to Tarski. It should be noted that Hofstadter references Turing MUCH more than Tarski, and Budiansky does just as much. On the other hand, Budiansky does critique GEB, noting that Hofstadter “far outran Gödel’s proof,” while at the same time it “contained not a word about the man himself.” Budiansky gets this right, but it would have been a good place here to insert at least a small note about Tarski.
Budiansky, besides remedying that, looks at Gödel’s actual reputation today in the worlds of science and philosophy. He says that in math, most modern mathematicians have seen little reason to venture past his barrier and that philosophy (as seemingly, Gödel himself) have found his theorem limiting.
One of the funniest quotes is one that stands in stark contrast to the famous Douglas Hofstadter book, “Gödel, Escher, Bach.” That is: “Bach and Wagner make me nervous.”
Not so funny is that, while Hofstadter had plenty of biographical elements about Bach, he had almost none about Escher and none on Gödel. This book remedies that in spades.
Gödel is best known for his Incompleteness Theorem, but on the math and philosophy side, had more than that, and “informed” discussions of relativity and more in physics.
Gödel had other oddities besides comment about Bach and Wagner. He was a diehard mathematical Platonist, but others exist today. That said, he seems to have been something like a diehard Platonist period.
That’s enough to give a good taste of this book, but without getting too deep into spoiler alert territory. Even clicking open the spoiler alert won't give all away.
That said, there are a couple of errata and issues in the book.
One minor one is that Budiansky claims Wiener schnitzel is really nothing more than cotoletta alla Milanese imported from Italy in the 1850s, allegedly by Radetsky. In 2007, a linguist totally debunked this.
The larger issue is one of omission. Many ideas that many people attribute to Gödel’s Incompleteness Theorem actually come from Tarski’s Undefinability Theorem. Tarski’s theorem extends beyond mathematics into semantics in general. That said, Budiansky isn’t alone. Realistically, Hofstadter should have written “Tarski, Escher, Bach.” That said, in turn, Gödel did apparently discover this first, but never published, so the technical credit goes to Tarski. It should be noted that Hofstadter references Turing MUCH more than Tarski, and Budiansky does just as much. On the other hand, Budiansky does critique GEB, noting that Hofstadter “far outran Gödel’s proof,” while at the same time it “contained not a word about the man himself.” Budiansky gets this right, but it would have been a good place here to insert at least a small note about Tarski.
Budiansky, besides remedying that, looks at Gödel’s actual reputation today in the worlds of science and philosophy. He says that in math, most modern mathematicians have seen little reason to venture past his barrier and that philosophy (as seemingly, Gödel himself) have found his theorem limiting.
October 4, 2021
An interesting biography of one of the great logicians of the 20th century. It details his childhood in Vienna, his escape from the Nazis, to his friendship with Albert Einstein at Princeton. The author provides a good explanation of his incompleteness theorems which can be quite daunting to those without a good background in mathematics, logic or philosophy but these sections are to provide an understanding of the importance of his work. The balance of the text is about the man, his life and the terrible events in Europe.
Some reviewers feel that there is too much detail in describing Vienna at the turn of the century but how events unfolded for those that were not murdered is frightful. It is such a shock to see how the cultured society changed overnight into thieves and blood thirsty brownshirts. I had a couple of friends who escaped from Vienna, ended up on a ship full of refugees that for months wandered from port to port and ended up in the far east before they were finally able to get passage to come to America. To they dying day, they said they would never go back to Vienna they had only terrible memories. The last section of the book also touches on why Godel would never go back and it resonates with the tales my friends told. The book "The Escape Of Sigmund Freud" is another interesting account of how Freud escaped from Vienna and the Nazis.
The book is in the same genre as "A Beautiful Mind" and "The Man Who Knew Infinity", if you liked these titles you will enjoy "Journey to the Edge of Reason". Sadly all of these geniuses were plagued with psychological problems of one kind or another yet were responsible for some of the most significant advances in math and logic in the first half of the 20th century.
Some reviewers feel that there is too much detail in describing Vienna at the turn of the century but how events unfolded for those that were not murdered is frightful. It is such a shock to see how the cultured society changed overnight into thieves and blood thirsty brownshirts. I had a couple of friends who escaped from Vienna, ended up on a ship full of refugees that for months wandered from port to port and ended up in the far east before they were finally able to get passage to come to America. To they dying day, they said they would never go back to Vienna they had only terrible memories. The last section of the book also touches on why Godel would never go back and it resonates with the tales my friends told. The book "The Escape Of Sigmund Freud" is another interesting account of how Freud escaped from Vienna and the Nazis.
The book is in the same genre as "A Beautiful Mind" and "The Man Who Knew Infinity", if you liked these titles you will enjoy "Journey to the Edge of Reason". Sadly all of these geniuses were plagued with psychological problems of one kind or another yet were responsible for some of the most significant advances in math and logic in the first half of the 20th century.
May 31, 2021
OK, I only got 1/3 of the way into this fascinating book before I was completely overwhelmed by the mathematics (and I mean just the simplified stuff in the text, not even the fuller accounts in the appendices). However, the account of Godel's background in the Austro-Hungarian Empire, with the Vienna Circle etc. is captivating, with lots of telling pen-portraits of Godel's contemporaries, such as Wittgenstein. This is a wonderful book, and one I will return to when I feel more courageous.
April 1, 2025
Stephen Budiansky's biography of Kurt Gödel is elegant and engaging. Journey to the Edge of Reason is balanced in a way its subject is not. Budiansky takes time to wander afield of Gödel to delve into the historical milieu, drawing parallels with Gödel state-of-mind and career milestones. The sections that explain Gödel's accomplishments in math and theory are clear and succinct, but I think they would have benefitted from a deeper attempt to make them legible to less mathematically and rationally inclined readers. I fear those sections, despite their smooth guiding pace, will stump many readers. This is unavoidable to some degree as there is often something paradoxically opaque about axioms. They often seem too content-less to be formal truth claims.
It is possible that this book deserved a deeper look at Gödel current influence on theoretical math, practical technology, and current philosophy (especially of the mind). Most of Budiansky's comments on this front are mere teasers. I raise this point because Erik Hoel's recent book takes time to consider whether incompleteness theory is useful as a description of the problem of consciousness. It is also interesting that Gödel's work hasn't come under more scrutiny (at least extrapolations from it) from rationalists and materialist. Maybe it has, I have have not been party to these conversations.
The critical takeaway for me was the importance of Gödel's social network. Without the staunch backing of von Neumann and Einstein, his story is likely to have ended much more tragically. It made me pine for a healthier and richer intellectual milieu and a more robust culture of mentorship and camaraderie among scientists. Additionally, it seems much of Gödel's talent were likely wasted or improperly directed.
It is possible that this book deserved a deeper look at Gödel current influence on theoretical math, practical technology, and current philosophy (especially of the mind). Most of Budiansky's comments on this front are mere teasers. I raise this point because Erik Hoel's recent book takes time to consider whether incompleteness theory is useful as a description of the problem of consciousness. It is also interesting that Gödel's work hasn't come under more scrutiny (at least extrapolations from it) from rationalists and materialist. Maybe it has, I have have not been party to these conversations.
The critical takeaway for me was the importance of Gödel's social network. Without the staunch backing of von Neumann and Einstein, his story is likely to have ended much more tragically. It made me pine for a healthier and richer intellectual milieu and a more robust culture of mentorship and camaraderie among scientists. Additionally, it seems much of Gödel's talent were likely wasted or improperly directed.
September 12, 2021
An enjoyable read about a mainly tragic figure. Strong points: it makes use of all the recently transcribed shorthand diaries and other interesting lesser-known material now available. So, it is seemingly definitive. Weak points: it really is a popular biography, so not much depth in the logical and philosophical material. The logical appendix on the Incompleteness Proof is ok.
My only "connection" to Gödel was that I attended a memorial gathering after his death at the Math Department at UCLA where several people who had known him spoke. My main recollection is a remark by Alonzo Church, who said that Gödel was "the only practicing solipsist" that he had ever known. Church is mentioned only briefly in the bio, and clearly did not know him well. One can imagine that in Gödel's bad times, he may have come off this way. Apparently for one lecture course he lectured facing the blackboard (without writing anything on it) the whole time. But one also gets the impression that he could be personable in his good times.
My only "connection" to Gödel was that I attended a memorial gathering after his death at the Math Department at UCLA where several people who had known him spoke. My main recollection is a remark by Alonzo Church, who said that Gödel was "the only practicing solipsist" that he had ever known. Church is mentioned only briefly in the bio, and clearly did not know him well. One can imagine that in Gödel's bad times, he may have come off this way. Apparently for one lecture course he lectured facing the blackboard (without writing anything on it) the whole time. But one also gets the impression that he could be personable in his good times.
April 22, 2024
I’ve always been a bit obsessed with mathematician and logician, Kurt Gödel. Mainly because he seemed to come at problems sideways, but admittedly also because he was a bit of a tragic hero: a man who battled mental illness (paranoid delusions and related self-starvation) for most of his life until it caused his death, but who also inspired Albert Einstein to continue attending the Institute for Advanced Studies at Princeton so Einstein could continue to enjoy their daily walks and talks.
Gödel is famous for his Incompleteness Theorem(s), which states that in any reasonable mathematical system there will always be true statements that cannot be proved. This implies that it might never be possible to achieve a complete understanding of the universe, or even a full understanding of the machines that we build (which seems prescient, as I write this in AI obsessed 2024). Practical findings to date support Gödel’s theories, but thankfully that hasn’t stopped the human race from trying to understand everything anyway!
There have been many books, book chapters, and articles on the life of Kurt Gödel. The gold standard remains ‘Logical Dilemmas: the life and works of Kurt Godel’ by John W Dawson (1997), which is based on the authors first-hand review of Gödel’s notes and letters, and which covers his work in far more breadth and depth than this latest biography. By comparison, ‘Edge of reason’ is written deliberately to be more accessible than previous biographies, and is targeted at a general public with an interest in popular science. It focuses more on Gödel’s struggles with nazism in his home Vienna and with his health than other biographies (though they all do mention these topics). In fact, one criticism I have read of ‘Edge of Reason’ is that there is too much historical context. I for one appreciated the context (especially in light of recent geo-socio-political events which feel rather familiar), but the point is taken. There IS a lot of history in here, but I liked it because said context not only marked (sometimes ended) the lives of the most talented collection of people to appear on our planet for many years, but it also shaped and drove the subsequent work of those who survived. Without the context, you just wouldn’t understand Gödel (or Einstein, von Neumann, and many others) anywhere near as well. However, I also accept that because Gödel was so painfully shy and socially anxious (he couldn’t teach, for this reason) there just isn’t that much to say about his life outside of his work (other than the rather tragic nature of his death). By comparison, with larger than life mathematician and physicist Johnny von Neumann (for example) there is an endless collection of outrageous anecdotes with which to entertain readers. In fact, you couldn’t get two more different people than Gödel and von Neumann, but they both contributed hugely despite their differences.
‘Edge of Reason’ is recommended, but if you are reasonably competent at (or interested in) science or maths you might like to give Logical Dilemmas a look.
NB: I listened to the audiobook on Audible. The narration is poor. Far too fast and without any attempt to give emphases where needed. Eg the narrator reads the title of the next chapter as if he is simply reading the next sentence. There is also no change in tone when reading a quotation. I slowed it down to 80% and it helped, but I will be avoiding the narrator in future.
Gödel is famous for his Incompleteness Theorem(s), which states that in any reasonable mathematical system there will always be true statements that cannot be proved. This implies that it might never be possible to achieve a complete understanding of the universe, or even a full understanding of the machines that we build (which seems prescient, as I write this in AI obsessed 2024). Practical findings to date support Gödel’s theories, but thankfully that hasn’t stopped the human race from trying to understand everything anyway!
There have been many books, book chapters, and articles on the life of Kurt Gödel. The gold standard remains ‘Logical Dilemmas: the life and works of Kurt Godel’ by John W Dawson (1997), which is based on the authors first-hand review of Gödel’s notes and letters, and which covers his work in far more breadth and depth than this latest biography. By comparison, ‘Edge of reason’ is written deliberately to be more accessible than previous biographies, and is targeted at a general public with an interest in popular science. It focuses more on Gödel’s struggles with nazism in his home Vienna and with his health than other biographies (though they all do mention these topics). In fact, one criticism I have read of ‘Edge of Reason’ is that there is too much historical context. I for one appreciated the context (especially in light of recent geo-socio-political events which feel rather familiar), but the point is taken. There IS a lot of history in here, but I liked it because said context not only marked (sometimes ended) the lives of the most talented collection of people to appear on our planet for many years, but it also shaped and drove the subsequent work of those who survived. Without the context, you just wouldn’t understand Gödel (or Einstein, von Neumann, and many others) anywhere near as well. However, I also accept that because Gödel was so painfully shy and socially anxious (he couldn’t teach, for this reason) there just isn’t that much to say about his life outside of his work (other than the rather tragic nature of his death). By comparison, with larger than life mathematician and physicist Johnny von Neumann (for example) there is an endless collection of outrageous anecdotes with which to entertain readers. In fact, you couldn’t get two more different people than Gödel and von Neumann, but they both contributed hugely despite their differences.
‘Edge of Reason’ is recommended, but if you are reasonably competent at (or interested in) science or maths you might like to give Logical Dilemmas a look.
NB: I listened to the audiobook on Audible. The narration is poor. Far too fast and without any attempt to give emphases where needed. Eg the narrator reads the title of the next chapter as if he is simply reading the next sentence. There is also no change in tone when reading a quotation. I slowed it down to 80% and it helped, but I will be avoiding the narrator in future.
February 3, 2022
Here’s what Brittanica says about Kurt Gödel: “Austrian-born mathematician, logician, and philosopher who obtained what may be the most important mathematical result of the 20th century: his famous incompleteness theorem, which states that within any axiomatic mathematical system there are propositions that cannot be proved or disproved on the basis of the axioms within that system; thus, such a system cannot be simultaneously complete and consistent. This proof established Gödel as one of the greatest logicians since Aristotle, and its repercussions continue to be felt and debated today.”
I learned so much, even though pretty much all the math was WAY over my head, because the author made it kinda sorta accessible to me, at least as far as generalities. More importantly for me was the clearly explained events leading to World Wars I and II primarily from the perspective of Austria and surrounding countries, starting in the 1850’s with the Hapsburg dynasty. Once laws limiting the Jews academically, professionally, and artistically had been abolished, those pesky Semites had risen to dominate those fields like a cork in a bucket of milk (a shout out to Annie Proulx for that metaphor). Resentments were unleashed and restrictions were reestablished, ultimately contributing to the holocaust. Gödel was able to make it to the US and eventually become a professor at Princeton and good friend of Einstein.
I also came out believing that genius is rarely only super high IQ, but often accompanied by eccentricities or even madness, as with Gödel. In middle age and later he was consumed by hypochondria and paranoia, believing all kinds of self made conspiracies against him, wouldn’t eat anything unless his wife-who had cooked his food-tasted each bite before she fed it to him. He weighed 65 pounds at the time is his death.
He also believed he could prove the US could be constitutionally turned into a dictatorship, an assertion still studies and debates today, fascinating, here’s the story as written in the New Yorker:
“The story goes that Gödel, while preparing for a U.S. citizenship test, in the nineteen-forties, imagined, in best Viennese form, that it would be a real test, not the pro forma examination it was. He studied the local laws ferociously—trying to learn why, in New Jersey, a township is distinguished from a borough—and buried himself in the Constitution, which he studied as though it were the “Principia Mathematica.” And he emerged confident that he had found a logical contradiction in the Constitution that could reverse democratic government itself. He shared this discovery with Einstein, and also with Oskar Morgenstern, the co-founder of game theory and a mutual friend; both men begged him not to make an issue of it during the test. But, at the ceremony, the judge asked Gödel where he came from, and he explained that he was from Austria, which had once been a democracy but was now a dictatorship. Isn’t it good that such a thing can’t happen here, the judge replied. “But it can!” Gödel declared. “I can prove it!””
“Gödel’s loophole, as some have called it, remains a mystery. He never defined it, and no trace of his discovery seems to linger in his papers. But he was far too exact a reader, and far too exacting a logician, not to have spotted something. Indeed, the question of Gödel’s loophole has inspired a remarkably large speculative literature, in serious scholarly journals as well as among scholars in this magazine, and recently among academics writing online. What was it? Probably not a loophole by which a Vice-President can simply refuse to recognize a slate of electors, during the Electoral College vote tally, and substitute one of his own choosing, thereby keeping his boss in power. That, presumably, was a bridge too far even for a logician. Dartmouth’s Dan Rockmore suggests that it might conceivably involve the contradictions of gerrymandering, which is constitutional but democracy-defeating, or the minority-empowering Electoral College. Another Gödel biographer, Jim Holt, turns to Harvard Law School’s distinguished professor emeritus, Laurence Tribe, suggesting that what Gödel had in mind was Article V of the Constitution, “since it sets no limits on how the Constitution can be amended.” Holt goes on,
‘The U.S. could be turned into a Constitutional dictatorship by a series of amendments. But it’s more interesting than that. Article 5 makes the document self-referential: it refers to “this Constitution.” It says, in effect, “I can be amended by such-and-such procedures.” And it seems to leave open the possibility that Article 5 itself is subject to amendment. This would permit a very direct route to dictatorship: amend it so that any diktat of the President is automatically an amendment.
“And that would, of course, be a neatly Gödelian recursive arrangement, of a sinister turn.
“But, when you think it through, there’s an overabundance of possible loopholes in the Constitution. The President is the Commander-in-Chief of the armed forces, with no named constraints; his power to act in that sphere is largely undefined and has altered significantly through the years, restrained sometimes by acts of Congress but mostly by assumptions that are not enumerated in the text, possibly because no one imagined that they would need to be. The President also possesses, under Article II, virtually unlimited pardon power for federal crimes, so he could, logically, have henchmen arrest or even kill elected federal officials who oppose him, and then pardon those same accomplices. Or, to take an instance in the opposite direction: the power of impeachment resides in the Congress, with the assumption that it is reserved for cases clearly involving a strong violation of law—a high crime or misdemeanor—so extreme that it alarms all sides. This has long been the case, and all three modern Presidential impeachments were treated as trials, with arguments, evidence, etc. But, given that high crimes and misdemeanors are not defined in the Constitution, and are effectively what a sufficient number of legislators decide they are, there is nothing to prevent impeachment from simply being an ejection seat: at any point when one party has a majority in the House and a two-thirds majority in the Senate, it can summarily expel the President by pure fiat.”
I learned so much, even though pretty much all the math was WAY over my head, because the author made it kinda sorta accessible to me, at least as far as generalities. More importantly for me was the clearly explained events leading to World Wars I and II primarily from the perspective of Austria and surrounding countries, starting in the 1850’s with the Hapsburg dynasty. Once laws limiting the Jews academically, professionally, and artistically had been abolished, those pesky Semites had risen to dominate those fields like a cork in a bucket of milk (a shout out to Annie Proulx for that metaphor). Resentments were unleashed and restrictions were reestablished, ultimately contributing to the holocaust. Gödel was able to make it to the US and eventually become a professor at Princeton and good friend of Einstein.
I also came out believing that genius is rarely only super high IQ, but often accompanied by eccentricities or even madness, as with Gödel. In middle age and later he was consumed by hypochondria and paranoia, believing all kinds of self made conspiracies against him, wouldn’t eat anything unless his wife-who had cooked his food-tasted each bite before she fed it to him. He weighed 65 pounds at the time is his death.
He also believed he could prove the US could be constitutionally turned into a dictatorship, an assertion still studies and debates today, fascinating, here’s the story as written in the New Yorker:
“The story goes that Gödel, while preparing for a U.S. citizenship test, in the nineteen-forties, imagined, in best Viennese form, that it would be a real test, not the pro forma examination it was. He studied the local laws ferociously—trying to learn why, in New Jersey, a township is distinguished from a borough—and buried himself in the Constitution, which he studied as though it were the “Principia Mathematica.” And he emerged confident that he had found a logical contradiction in the Constitution that could reverse democratic government itself. He shared this discovery with Einstein, and also with Oskar Morgenstern, the co-founder of game theory and a mutual friend; both men begged him not to make an issue of it during the test. But, at the ceremony, the judge asked Gödel where he came from, and he explained that he was from Austria, which had once been a democracy but was now a dictatorship. Isn’t it good that such a thing can’t happen here, the judge replied. “But it can!” Gödel declared. “I can prove it!””
“Gödel’s loophole, as some have called it, remains a mystery. He never defined it, and no trace of his discovery seems to linger in his papers. But he was far too exact a reader, and far too exacting a logician, not to have spotted something. Indeed, the question of Gödel’s loophole has inspired a remarkably large speculative literature, in serious scholarly journals as well as among scholars in this magazine, and recently among academics writing online. What was it? Probably not a loophole by which a Vice-President can simply refuse to recognize a slate of electors, during the Electoral College vote tally, and substitute one of his own choosing, thereby keeping his boss in power. That, presumably, was a bridge too far even for a logician. Dartmouth’s Dan Rockmore suggests that it might conceivably involve the contradictions of gerrymandering, which is constitutional but democracy-defeating, or the minority-empowering Electoral College. Another Gödel biographer, Jim Holt, turns to Harvard Law School’s distinguished professor emeritus, Laurence Tribe, suggesting that what Gödel had in mind was Article V of the Constitution, “since it sets no limits on how the Constitution can be amended.” Holt goes on,
‘The U.S. could be turned into a Constitutional dictatorship by a series of amendments. But it’s more interesting than that. Article 5 makes the document self-referential: it refers to “this Constitution.” It says, in effect, “I can be amended by such-and-such procedures.” And it seems to leave open the possibility that Article 5 itself is subject to amendment. This would permit a very direct route to dictatorship: amend it so that any diktat of the President is automatically an amendment.
“And that would, of course, be a neatly Gödelian recursive arrangement, of a sinister turn.
“But, when you think it through, there’s an overabundance of possible loopholes in the Constitution. The President is the Commander-in-Chief of the armed forces, with no named constraints; his power to act in that sphere is largely undefined and has altered significantly through the years, restrained sometimes by acts of Congress but mostly by assumptions that are not enumerated in the text, possibly because no one imagined that they would need to be. The President also possesses, under Article II, virtually unlimited pardon power for federal crimes, so he could, logically, have henchmen arrest or even kill elected federal officials who oppose him, and then pardon those same accomplices. Or, to take an instance in the opposite direction: the power of impeachment resides in the Congress, with the assumption that it is reserved for cases clearly involving a strong violation of law—a high crime or misdemeanor—so extreme that it alarms all sides. This has long been the case, and all three modern Presidential impeachments were treated as trials, with arguments, evidence, etc. But, given that high crimes and misdemeanors are not defined in the Constitution, and are effectively what a sufficient number of legislators decide they are, there is nothing to prevent impeachment from simply being an ejection seat: at any point when one party has a majority in the House and a two-thirds majority in the Senate, it can summarily expel the President by pure fiat.”
April 27, 2025
Very nice, and highly readable even for non mathematicians. Budiansky captures the convergence of mathematical abstraction, philosophical inquiry, and existential fragility, presenting a deeply textured portrait of a mind both brilliant and later, tormented.
I was very interested to read about Godels own insecurities and eccentricities that seem typical of all brilliant minds. Any scientist would benefit from reading this text.
I was very interested to read about Godels own insecurities and eccentricities that seem typical of all brilliant minds. Any scientist would benefit from reading this text.
June 15, 2023
Kurt Gödel was a legendary man. At the tender age of 25, he proved two groundbreaking theorems. They are called the incompleteness theorems and shattered Hilbert's hope of finding a complete and consistent set of axioms for all mathematics. The first incompleteness theorem states that any sufficiently complex system of mathematics has unprovable statements. The second incompleteness theorem shows that the system cannot demonstrate its consistency. When a system is consistent, it doesn't lead to logical contradictions.
The book begins at the end of Gödel's life. Gödel's confidence in his reasoning abilities and his ability to keep pace with his coworkers at the Institute for Advanced Studies began to waver. I believe the term is "Publish or Perish." Although he published the incompleteness theorems, those happened 40 years before. Gödel feared poisoning and would only eat food made by his wife, Adele. When Gödel died, he weighed only 29 kilograms or 65 pounds.
Austria had long been a melting pot of culture. World War I upended all of that. The loss of financial stability led to the long-standing anti-Semitism in Europe festering. Author Stephen Budiansky does not get to the point immediately. I assumed the author would get the section leading to Gödel's birth over within a few paragraphs. The author does a great job explaining everything. I suppose Budiansky wanted to establish a parallel with Gödel and Austria.
Eventually, the anti-Semitism was so terrible that Gödel emigrated to the United States. He would spend the rest of his life employed by the Institute for Advanced Studies, an offshoot of Princeton University.
I enjoyed the book. I did know some things about Gödel from other books, but Budiansky does a great job of establishing what Gödel did for mathematics. Thanks for reading my review, and see you next time.
The book begins at the end of Gödel's life. Gödel's confidence in his reasoning abilities and his ability to keep pace with his coworkers at the Institute for Advanced Studies began to waver. I believe the term is "Publish or Perish." Although he published the incompleteness theorems, those happened 40 years before. Gödel feared poisoning and would only eat food made by his wife, Adele. When Gödel died, he weighed only 29 kilograms or 65 pounds.
Austria had long been a melting pot of culture. World War I upended all of that. The loss of financial stability led to the long-standing anti-Semitism in Europe festering. Author Stephen Budiansky does not get to the point immediately. I assumed the author would get the section leading to Gödel's birth over within a few paragraphs. The author does a great job explaining everything. I suppose Budiansky wanted to establish a parallel with Gödel and Austria.
Eventually, the anti-Semitism was so terrible that Gödel emigrated to the United States. He would spend the rest of his life employed by the Institute for Advanced Studies, an offshoot of Princeton University.
I enjoyed the book. I did know some things about Gödel from other books, but Budiansky does a great job of establishing what Gödel did for mathematics. Thanks for reading my review, and see you next time.
June 27, 2021
This is a fantastic biography on Czech/Austrian mathematician Kurt Gödel, who Albert Einstein called the greatest logician since Aristotle. I thought the author beautifully set the stage with an extended introduction about the Austro-Hungarian empire, its dissolution following World War 1, and how this impacted the atmosphere in which Gödel came of age in the early 1900s. The book was very well researched and was a more compelling read than other books on Gödel that I’ve read. If there was one weakness, it would be that some of the mathematical concepts were explained in a confusing manner. I’d highly recommend this book to anyone interested in learning more about the man behind maybe the most important mathematical result of the 20th century.
August 20, 2021
3.5 stars
I enjoyed parts of this book, however I don't think it was one that had much impact. It was short and that's both positive and negative because biographies can be massive unreadable tomes. At some points, I felt that Budiansky was writing more of the history of Austria-Hungarian empire and Princeton/ The Institute for Higher Learning or the eccentricities of Wittegenstein then Gödel. It was interesting stuff but he spent more time contextualizing Gödel than parts of his life, some which were hurried through. He described Gödel's main work succinctly and made it as approachable as possible for the lay reader. Overall, it wasn't badly written but a tad dry.
Writing: C
Research: B
Accuracy: A
Premise: B
I enjoyed parts of this book, however I don't think it was one that had much impact. It was short and that's both positive and negative because biographies can be massive unreadable tomes. At some points, I felt that Budiansky was writing more of the history of Austria-Hungarian empire and Princeton/ The Institute for Higher Learning or the eccentricities of Wittegenstein then Gödel. It was interesting stuff but he spent more time contextualizing Gödel than parts of his life, some which were hurried through. He described Gödel's main work succinctly and made it as approachable as possible for the lay reader. Overall, it wasn't badly written but a tad dry.
Writing: C
Research: B
Accuracy: A
Premise: B
April 13, 2025
Calling it - DNF @ 66%. I was listening to this on 1.5x while at the gym, and although I enjoyed the intro, on Gödel’s mental health issues at the end of his life, and the background on Austria that followed, the math writing is just not translating to the audiobook format, and the historical elements are getting too bleak for me.
The math writing probably worked on the page but fully failed when just read straight out. It wasn’t on the narrator - I think you just can’t read math out loud that way! And there wasn’t enough in-depth explanation of where the mathematical world was at that time. Mathematicians were selling out lecture halls! I think there’s a lot more that could have been discussed about the historical developments of math that the author didn’t choose to unpack. Pretty disappointing.
I also got the feeling that there maybe just wasn’t enough info out there on Gödel himself to fill an entire biography - thus all the historical/political context. He didn’t write down much of what he was dealing with and purposefully eg didn’t keep documentation re his time in various sanitariums. Maybe it’s the case that if you wanted to turn the available information on him into a compelling story, you would have to do it in fiction. But I was surprised that the author would drop in occasional nuggets of real interest - Gödel’s relationship with his wife, who was apparently older, unattractive, fat, and extremely funny and charming, and with whom Gödel apparently had a very interesting sex life, for example! - and then quickly move on.
Also, the writing on Gödel’s mental health issues (likely some form of OCD) feels as though it’s external reporting on a topic that is (a) outside the author’s experience, and (b) outside what the author has any interest in experiencing, even vicariously. You have to ask yourself what the point is of writing a biography if the biographer is keeping themself at such arms length that the subject feels almost more remote and unknowable than they did before you started reading.
It seems to me as though this author maybe wanted to write about the mathematicians in Vienna in the 1920s and 1930s and how they were affected by their political context, and Gödel was a good hook. Which is fine. But I think it’s a shame because there are some really interesting questions to consider re. Gödel and his work/life in particular, and this book promises that consideration - and then fails to deliver.
The math writing probably worked on the page but fully failed when just read straight out. It wasn’t on the narrator - I think you just can’t read math out loud that way! And there wasn’t enough in-depth explanation of where the mathematical world was at that time. Mathematicians were selling out lecture halls! I think there’s a lot more that could have been discussed about the historical developments of math that the author didn’t choose to unpack. Pretty disappointing.
I also got the feeling that there maybe just wasn’t enough info out there on Gödel himself to fill an entire biography - thus all the historical/political context. He didn’t write down much of what he was dealing with and purposefully eg didn’t keep documentation re his time in various sanitariums. Maybe it’s the case that if you wanted to turn the available information on him into a compelling story, you would have to do it in fiction. But I was surprised that the author would drop in occasional nuggets of real interest - Gödel’s relationship with his wife, who was apparently older, unattractive, fat, and extremely funny and charming, and with whom Gödel apparently had a very interesting sex life, for example! - and then quickly move on.
Also, the writing on Gödel’s mental health issues (likely some form of OCD) feels as though it’s external reporting on a topic that is (a) outside the author’s experience, and (b) outside what the author has any interest in experiencing, even vicariously. You have to ask yourself what the point is of writing a biography if the biographer is keeping themself at such arms length that the subject feels almost more remote and unknowable than they did before you started reading.
It seems to me as though this author maybe wanted to write about the mathematicians in Vienna in the 1920s and 1930s and how they were affected by their political context, and Gödel was a good hook. Which is fine. But I think it’s a shame because there are some really interesting questions to consider re. Gödel and his work/life in particular, and this book promises that consideration - and then fails to deliver.
October 11, 2024
Somewhat rewarding book in the sense that it gives you a very good description of Godel as a human and his life experiences. This is drily described so you still don't fully get a sense of who Godel was as a person. The subject matter of his contributions is shown only as a reflection of his life experiences though the appendix does explain the Incompleteness Theorem (for a better exposition you need to read Godel's Proof by Nagel and Newman). Overall a book worth reading.
June 9, 2023
Surprisingly good. The author focuses more on the culture around Gödel rather than on the man himself which makes the book all the more interesting. Will write a longer review later.
August 18, 2021
This is an excellent book. It covers the time period of Godel's life, and the people surrounding him, as much as it does Godel. This is something I appreciated. I learned much about the fall of Austria to Naziism and the formation of the Institute for Advanced Study. Also interesting tidbits about other mathematicians - John von Neuman's prodigious memory and Paul Cohen's worries that his proofs of the independence of the Continuum Hypothesis and Axiom of Choice might be flawed, and his reaching out to Godel for a critical review before publication.
For those who might be hesitant, there is little to no real mathematics in this book. What discussion of math there is concerns itself with helping the reader understand just how unexpected and earth-shaking Godel's results were.
One thing I would like to have seen is some discussion of just how Godel came up with the Incompleteness Theorem. Did he somehow intuit that mathematical systems could not prove their own consistency or completeness? Or did he only get there after multiple failed attempts to prove the opposite? But there may not be any source material to work from related to this.
For those who might be hesitant, there is little to no real mathematics in this book. What discussion of math there is concerns itself with helping the reader understand just how unexpected and earth-shaking Godel's results were.
One thing I would like to have seen is some discussion of just how Godel came up with the Incompleteness Theorem. Did he somehow intuit that mathematical systems could not prove their own consistency or completeness? Or did he only get there after multiple failed attempts to prove the opposite? But there may not be any source material to work from related to this.
July 6, 2021
The first half of the book is more about Vienna before the Anschluss and the Vienna Circle than Godel in particular. Red Vienna before the 1930s was a contentious polarized but an intellectually thriving place in Art, Philosophy, and Science (although failing politically). It was swept away by the fascists (Make Austria Great Again) and the Anschluss Godel proved his incompleteness theorem in this hothouse foreclosing the possibility of an all-encompassing axiomatic foundation or having any system of mathematics reaching every possible truth. Some trust is beyond whatever axiomatic scheme that we construct.
The second half is set at Princeton which Godel settled down in, to escape the thirties MAGA of Adolf Hitler. Although his time was still fruitful he was plagued by hypochondria and paranoia. An eccentric character who was rather hard to get to know but a genius who if a little more extraverted would have had more of his works shared.
The second half is set at Princeton which Godel settled down in, to escape the thirties MAGA of Adolf Hitler. Although his time was still fruitful he was plagued by hypochondria and paranoia. An eccentric character who was rather hard to get to know but a genius who if a little more extraverted would have had more of his works shared.
April 16, 2022
A well written, deeply researched biography of perhaps the most creative and original mathematical thinker in modern times. One of Albert Einstein’s closest confidants late in his life, Gödel was also troubled by increasing bouts of mental illness. One might be tempted to lump Gödel into the stereotype of the troubled genius, à la Van Gogh, despite innumerable counter-examples like Einstein or Picasso; though I’d hope not, as this diminishes Gödel’s unique personality and humanity.
The author does a great job of describing the societal upheavals (especially the rise of fascism) that Gödel—and his Vienna Circle—were experiencing and how those upheavals impacted Gödel’s life choices (cf., Sigmund’s “Exact Thinking in Demented Times”).
The book also does a pretty good job of explaining Gödel’s famous Incompleteness Theorem, no mean feat (I heartily recommend “Gödel’s Proof” by Nagel & Newman for a more complete layman’s treatment).
The author does a great job of describing the societal upheavals (especially the rise of fascism) that Gödel—and his Vienna Circle—were experiencing and how those upheavals impacted Gödel’s life choices (cf., Sigmund’s “Exact Thinking in Demented Times”).
The book also does a pretty good job of explaining Gödel’s famous Incompleteness Theorem, no mean feat (I heartily recommend “Gödel’s Proof” by Nagel & Newman for a more complete layman’s treatment).
September 13, 2021
Interesting biography that mostly demystifies Gödel by placing his live in a deeper historical context and his work in a more specific context. I read it because of the anorexia angle, but enjoyed the math part a lot more. Overall, not a strong recommendation unless you are very into turn of the century math and logic, Princeton, or weird academic wives.
July 1, 2021
Brilliant description of Kurt Goedel's groundbreaking rethinking of mathematics in the 1930s, along with a well written biography of a complex, brilliant mathematician, whose work is still in vogue 90 years later.
June 5, 2021
wealth of (personal) anecdotes (which is important), poverty of, and (what is not the same thing) startling conventionality of, reflection. good use of archival materials.
April 8, 2023
Interesting work. The first several chapters could almost stand on their own as a history of Austria for the several decades leading up to WW2. These were shocking to read -- the anti-Semitism amongst scientists in the Austrian university system was incomprehensible. The book includes an excerpt of an evaluation of Godel's application for a position at the University of Vienna (Godel was an Austrian, but not Jewish) in which the comments from the evaluator are almost entirely about his association with Jews and how his dissertation work was conducted under a Jewish supervisor, etc. This was meant to illustrate the general anti-Jewish sentiment of the time. I wonder what mental gymnastics those academics did in order to convince themselves that scientific scholarship by Jews was somehow less ... important? correct? worthy? Any clear-thinking scientist should know better. Of course, the whole premise of this part of the book is to show that they are not clear-thinking scientists, they were eventual supporters of the Fascist regime.
The book mentions how the Jews in Austria took full advantage of the opportunities made available to them for education (after having been long denied) and therefore began to constitute a large number of faculty members and students at the prestigious universities. This (among other things) led to the anti-Semitism mentioned above. It reminds me how there have been complaints of "too many" Asian-American students at prestigious American universities. How can there be "too many"?
Of course, the whole transition from a society that valued education and tolerance moving to one of nationalism and anti-liberalism seems a very close parallel to today's trends with members of Congress trying to re-normalize anti-Semitism and all the anti-"woke" rhetoric which is just a way of cloaking intolerance in favor of white nationalism.
Anyway, so about Godel ... this part was also compelling namely for the way it aptly illustrated Godel's dual nature of extreme rationalism and paranoia, and how they were connected. On the one hand, I am grateful for what Godel was able to contribute to science, despite his psychological challenges. On the other hand, what else might he have accomplished if he had been able to overcome his paranoia and hypochondria? The book creates a feeling of pathos for Godel, watching his deterioration step by step, but still seeing flashes of brilliance now and again.
To end on a lighter note, I loved the story of Godel's interview for his American citizenship application. Just the whole idea of his friend picking Godel up in his car, driving over to pick up Einstein, and the 3 of them riding together while Einstein makes a joke about whether Godel was prepared or not was hilarious. And of course the constitutional contradiction part too.
The book mentions how the Jews in Austria took full advantage of the opportunities made available to them for education (after having been long denied) and therefore began to constitute a large number of faculty members and students at the prestigious universities. This (among other things) led to the anti-Semitism mentioned above. It reminds me how there have been complaints of "too many" Asian-American students at prestigious American universities. How can there be "too many"?
Of course, the whole transition from a society that valued education and tolerance moving to one of nationalism and anti-liberalism seems a very close parallel to today's trends with members of Congress trying to re-normalize anti-Semitism and all the anti-"woke" rhetoric which is just a way of cloaking intolerance in favor of white nationalism.
Anyway, so about Godel ... this part was also compelling namely for the way it aptly illustrated Godel's dual nature of extreme rationalism and paranoia, and how they were connected. On the one hand, I am grateful for what Godel was able to contribute to science, despite his psychological challenges. On the other hand, what else might he have accomplished if he had been able to overcome his paranoia and hypochondria? The book creates a feeling of pathos for Godel, watching his deterioration step by step, but still seeing flashes of brilliance now and again.
To end on a lighter note, I loved the story of Godel's interview for his American citizenship application. Just the whole idea of his friend picking Godel up in his car, driving over to pick up Einstein, and the 3 of them riding together while Einstein makes a joke about whether Godel was prepared or not was hilarious. And of course the constitutional contradiction part too.
July 2, 2021
What I liked about this book is the historical detail it allows itself to slip into. I bought it for a friend studying IT/Informatik in Vienna, thinking it would be very fitting. I, myself, listened to the entirety of it on Audible and found the voice actor pretty bad, especially in pronouncing German. So I recommend getting a physical copy.
The mathematics in the book are well summarised in an impressive video by the YouTube channel Veritasium: https://youtu.be/HeQX2HjkcNo
My initial reaction on watching the video: “But what Gödel did for mathematics only, Popper did for the whole of science and the problem-solving of life.” What I meant by that is that Gödel proved via his theorem the necessary incompleteness of all mathematics; the same way Popper proved the a priori creativity of scientific progress, and that without incompleteness science cannot advance, because a theory must always be falsifiable/disprovable/create problems to solve.
Popper would agree with Gödel's statement: “for clear questions posed by reason, reason can also find clear answers.” Both could be classified as what Robert Voegelin calls “Westcoast skeptics”, opposed to Eastcoast skeptics, finding the fact of our limited knowledge liberating, especially for human creativity.
After a brief comparison of Gödel’s concept of truth, a more in-depth analysis of that of Popper’s is to follow.
Gödel’s world view seems to be that we can intuit true (i.e. existing) things that we don’t have a logical justification for and cannot mathematically derive at in any system.
Karl Popper, on the other hand, doesn’t believe in that kind of “truth”. Popper subscribes to the correspondence theory of truth: truth is what the facts are.
He borrows Alfred Tarski’s definition:
“p” is true if and only if p.
claiming that A HYPOTHESIS is all that “p” is. Our intuitions are only hypotheses and we have no grounds for seeing them as truths in Gödel’s sense. Our brain is analogous to a theory, having tentatively evolved through instruction and selection (Gödel didn’t believe in evolution), and our conscious experience brings new hypotheses into being, without them having any necessary correspondence with the real world or any existing things in the universe (that we “directly” perceive neither presently, through a process of induction akin to Gödel’s view of how we derive at true mathematical axioms, nor in the past, like Plato’s forms, nor in the future, like the communist society). No idea that we can believe in or grasp is essentially and in its purest form “behind” our factual, corroborating instances of the hypothesis, in the “real” world; of course ideas aren't literally identical with any physical things; this is Popper’s critique of essentialism. Gödel’s logic applies here: “I don’t see any reason why we should have less confidence in this kind of perception, that is, in mathematical intuition, than in sense perception …” (last chapter). Here, Gödel puts both areas of inquiry on an equal footing (albeit to make an unwarranted point in favour of idealism).
In describing theories as “closer to the truth”, what Popper means by truth is yet another thing. The sum of our experimental results, if they are positive, corroborating tests, will make a theory acceptable (= closer to the truth; note that this notion of the truth cannot directly correspond or be identical with the level of facts and experimental outcomes which are relevant to them, hence “closer to”).
Not, however, worthy of being believed in. The role of science is often to “overthrow this worthiness”, according to Popper’s own words, never establishing it. (See The Myth of the Framework)
With this last notion of truth, Popper is trying to reconcile the vocabulary used for an acceptable theory with that used for a fact. Popper does not deny that there might also be use for unfalsifiable statements — which may or may not be true, though this can, by definition, not be known — which can be criticised (though often people do not allow themselves to question or criticise such statements or even elicit implicitly held taboos that can take the form of unfalsifiable statements). My philosophy falls into the category of the unfalsifiable. As does Popper’s, as he readily admits; Popper proposes a sort of pragmatic philosophy for the scientist to adhere to, a program I sympathise with, because I do believe it has had a positive cultural impact. No one can ‘disprove’ our problem-solving methods since what we are talking about aren’t real things. Popper insists that, in science, we attempt to talk about real things. That’s why he uses the words “truth” and “truth-like”. This is a difference between science and philosophy. Yet philosophy (e.g. epistemology) and science, I argue with Popper, have in common that they are both oriented toward problem-solving.
Thus, down to its bare bones, Popper’s idea of truth, as addressed to his readers, constitutes merely the human claims that potentially attain a certain status as “truth” or acceptability in the eyes of the (scientific) community or in those of a mere individual (rebelling against a community), *rather than explicitly stating that any concept of why a theory is true originates with the believer and, therefore, that this criterion is asserted by a member of the community and is imaginary.* His philosophy denies that there is any criterium that can generally decide on whether something is true or truth-like and he admits that truth-claims are impositions by the individual onto the world (to some extent following Immanuel Kant). Thus, often in his writings, he completely circumnavigates the issue of belief, implicitly and explicitly acknowledging the creativity of human beings. This creates the impression, for me at least, that he ascribes to the statement between asterisks above, without clearly stating it, to provide with a philosophy of science that general readers can come to an agreement on, mentioned in the previous paragraph.
I suppose telling a lie only requires being unaware of the fact of the imposition one is making when asserting a claim; because that is sufficient for a person to appeal to an authority as source of truth. The only source of truth is you.
For Popper the problem of science is a problem in epistemology: “how do I know what I know?”
What distinguishes that from the problem addressed by nihilism is that ours is the problem of belief, asserting: “there is nothing to be believed in”. (Extending Popper’s critique of worthiness for belief in scientific theories or theories *about knowledge*, mentioned above, to all belief. Note: people usually justify their belief by claiming to know about the existence or “truth” of the things they believe in, otherwise they see themselves and others as acting hypocritically. If someone has no sense of the objective [this can have ontogenetic reasons], or doesn’t value truth, that makes them less susceptible to care about either criticism.) While Gödel isn’t alone in this, it is interesting to note that he describes nihilism as “grim”.
The program of nihilism is much more extended than Popper’s philosophy of science. To my knowledge, Popper never rejected belief systematically in writing. His attitude, like that of many skeptics, nevertheless is indicative of such a rejection and the creativity that comes with it.
The reader may compare what I say here with what I have to say in my video “Against Belief”: https://youtu.be/qjcAaDqkzMY
The mathematics in the book are well summarised in an impressive video by the YouTube channel Veritasium: https://youtu.be/HeQX2HjkcNo
My initial reaction on watching the video: “But what Gödel did for mathematics only, Popper did for the whole of science and the problem-solving of life.” What I meant by that is that Gödel proved via his theorem the necessary incompleteness of all mathematics; the same way Popper proved the a priori creativity of scientific progress, and that without incompleteness science cannot advance, because a theory must always be falsifiable/disprovable/create problems to solve.
Popper would agree with Gödel's statement: “for clear questions posed by reason, reason can also find clear answers.” Both could be classified as what Robert Voegelin calls “Westcoast skeptics”, opposed to Eastcoast skeptics, finding the fact of our limited knowledge liberating, especially for human creativity.
After a brief comparison of Gödel’s concept of truth, a more in-depth analysis of that of Popper’s is to follow.
Gödel’s world view seems to be that we can intuit true (i.e. existing) things that we don’t have a logical justification for and cannot mathematically derive at in any system.
Karl Popper, on the other hand, doesn’t believe in that kind of “truth”. Popper subscribes to the correspondence theory of truth: truth is what the facts are.
He borrows Alfred Tarski’s definition:
“p” is true if and only if p.
claiming that A HYPOTHESIS is all that “p” is. Our intuitions are only hypotheses and we have no grounds for seeing them as truths in Gödel’s sense. Our brain is analogous to a theory, having tentatively evolved through instruction and selection (Gödel didn’t believe in evolution), and our conscious experience brings new hypotheses into being, without them having any necessary correspondence with the real world or any existing things in the universe (that we “directly” perceive neither presently, through a process of induction akin to Gödel’s view of how we derive at true mathematical axioms, nor in the past, like Plato’s forms, nor in the future, like the communist society). No idea that we can believe in or grasp is essentially and in its purest form “behind” our factual, corroborating instances of the hypothesis, in the “real” world; of course ideas aren't literally identical with any physical things; this is Popper’s critique of essentialism. Gödel’s logic applies here: “I don’t see any reason why we should have less confidence in this kind of perception, that is, in mathematical intuition, than in sense perception …” (last chapter). Here, Gödel puts both areas of inquiry on an equal footing (albeit to make an unwarranted point in favour of idealism).
In describing theories as “closer to the truth”, what Popper means by truth is yet another thing. The sum of our experimental results, if they are positive, corroborating tests, will make a theory acceptable (= closer to the truth; note that this notion of the truth cannot directly correspond or be identical with the level of facts and experimental outcomes which are relevant to them, hence “closer to”).
Not, however, worthy of being believed in. The role of science is often to “overthrow this worthiness”, according to Popper’s own words, never establishing it. (See The Myth of the Framework)
With this last notion of truth, Popper is trying to reconcile the vocabulary used for an acceptable theory with that used for a fact. Popper does not deny that there might also be use for unfalsifiable statements — which may or may not be true, though this can, by definition, not be known — which can be criticised (though often people do not allow themselves to question or criticise such statements or even elicit implicitly held taboos that can take the form of unfalsifiable statements). My philosophy falls into the category of the unfalsifiable. As does Popper’s, as he readily admits; Popper proposes a sort of pragmatic philosophy for the scientist to adhere to, a program I sympathise with, because I do believe it has had a positive cultural impact. No one can ‘disprove’ our problem-solving methods since what we are talking about aren’t real things. Popper insists that, in science, we attempt to talk about real things. That’s why he uses the words “truth” and “truth-like”. This is a difference between science and philosophy. Yet philosophy (e.g. epistemology) and science, I argue with Popper, have in common that they are both oriented toward problem-solving.
Thus, down to its bare bones, Popper’s idea of truth, as addressed to his readers, constitutes merely the human claims that potentially attain a certain status as “truth” or acceptability in the eyes of the (scientific) community or in those of a mere individual (rebelling against a community), *rather than explicitly stating that any concept of why a theory is true originates with the believer and, therefore, that this criterion is asserted by a member of the community and is imaginary.* His philosophy denies that there is any criterium that can generally decide on whether something is true or truth-like and he admits that truth-claims are impositions by the individual onto the world (to some extent following Immanuel Kant). Thus, often in his writings, he completely circumnavigates the issue of belief, implicitly and explicitly acknowledging the creativity of human beings. This creates the impression, for me at least, that he ascribes to the statement between asterisks above, without clearly stating it, to provide with a philosophy of science that general readers can come to an agreement on, mentioned in the previous paragraph.
I suppose telling a lie only requires being unaware of the fact of the imposition one is making when asserting a claim; because that is sufficient for a person to appeal to an authority as source of truth. The only source of truth is you.
For Popper the problem of science is a problem in epistemology: “how do I know what I know?”
What distinguishes that from the problem addressed by nihilism is that ours is the problem of belief, asserting: “there is nothing to be believed in”. (Extending Popper’s critique of worthiness for belief in scientific theories or theories *about knowledge*, mentioned above, to all belief. Note: people usually justify their belief by claiming to know about the existence or “truth” of the things they believe in, otherwise they see themselves and others as acting hypocritically. If someone has no sense of the objective [this can have ontogenetic reasons], or doesn’t value truth, that makes them less susceptible to care about either criticism.) While Gödel isn’t alone in this, it is interesting to note that he describes nihilism as “grim”.
The program of nihilism is much more extended than Popper’s philosophy of science. To my knowledge, Popper never rejected belief systematically in writing. His attitude, like that of many skeptics, nevertheless is indicative of such a rejection and the creativity that comes with it.
The reader may compare what I say here with what I have to say in my video “Against Belief”: https://youtu.be/qjcAaDqkzMY
October 26, 2025
S Kurtem Gödelem jsem mentálně strávil několik týdnů. A naučil jsem se od něj nejen principům jeho velmi elegantního důkazu vět o neúplnosti.
K(urt) rozhodně nebyl natolik společenský jako třeba von Neumann, přesto byl hluboce ovlivněn vazbami na několik svých blízkých. Ti i on sám nám pak skrze své dopisy a texty dávají nahlédnout do mysli tohoto génia – extrémní preciznost ho na jedné straně dostala na piedestal největších logiků historie, ale na straně druhé mu také způsobila četné psychické potíže. Zdá se, že se opravdu jedná o dvě strany téže mince. A stejně tak se to děje i u charakterových vlastností každého z nás; nelze si vybrat jen tu jednu, co se nám více hodí. V důsledku je pak na nás, jak se s nimi oběma dokážeme vyrovnat. Zvládl to on?
Skrze jeho životní příběh jsem si také připomněl, jak zásadně historické události formovaly osudy těch žijících v průběhu 20. století: Gödelova rodina žila z rozkvětu textilek (zdánlivě nekonečně stabilního) rakousko-uherského mocnářství, mládí strávil jako německý Brňák v (tehdy ještě nadnárodním) Československu, pro svá formující léta se přestěhoval do (kulturně a vědecky neskutečně pulzující) Wien, aby nakonec během války uprchl z (Hitlerem už ovládaného) Rakouska a dobrou polovinu svého života strávil na Institutu v (drtivě maloměstském) Princeton. Navíc mi Budiansky nabídl – pro mě nezvyklý – americký pohled na tyto reálie střední Evropy první poloviny minulého století.
Odkaz Kurta Gödela na první pohled tkví v jeho převratných myšlenkách o limitách lidského poznání, které navždy změnily matematiku a – prostřednictvím počítačové vědy – moderní svět okolo nás. Pro mne je však především někým, kdo věřil v "nenahraditelnou jedinečnost lidského ducha" a pomohl přemýšlet o světě v širokých souvislostech i takovým myslitelům jako Albert Einstein. A také někým, kdo chtěl při skládání zkoušky pro přidělení amerického občanství soudci ukázat logické chyby v ústavě USA, díky kterým "by bylo možné, aby se někdo stal naprosto legálním způsobem diktátorem a nastolil fašistický režim".
K(urt) rozhodně nebyl natolik společenský jako třeba von Neumann, přesto byl hluboce ovlivněn vazbami na několik svých blízkých. Ti i on sám nám pak skrze své dopisy a texty dávají nahlédnout do mysli tohoto génia – extrémní preciznost ho na jedné straně dostala na piedestal největších logiků historie, ale na straně druhé mu také způsobila četné psychické potíže. Zdá se, že se opravdu jedná o dvě strany téže mince. A stejně tak se to děje i u charakterových vlastností každého z nás; nelze si vybrat jen tu jednu, co se nám více hodí. V důsledku je pak na nás, jak se s nimi oběma dokážeme vyrovnat. Zvládl to on?
Skrze jeho životní příběh jsem si také připomněl, jak zásadně historické události formovaly osudy těch žijících v průběhu 20. století: Gödelova rodina žila z rozkvětu textilek (zdánlivě nekonečně stabilního) rakousko-uherského mocnářství, mládí strávil jako německý Brňák v (tehdy ještě nadnárodním) Československu, pro svá formující léta se přestěhoval do (kulturně a vědecky neskutečně pulzující) Wien, aby nakonec během války uprchl z (Hitlerem už ovládaného) Rakouska a dobrou polovinu svého života strávil na Institutu v (drtivě maloměstském) Princeton. Navíc mi Budiansky nabídl – pro mě nezvyklý – americký pohled na tyto reálie střední Evropy první poloviny minulého století.
Odkaz Kurta Gödela na první pohled tkví v jeho převratných myšlenkách o limitách lidského poznání, které navždy změnily matematiku a – prostřednictvím počítačové vědy – moderní svět okolo nás. Pro mne je však především někým, kdo věřil v "nenahraditelnou jedinečnost lidského ducha" a pomohl přemýšlet o světě v širokých souvislostech i takovým myslitelům jako Albert Einstein. A také někým, kdo chtěl při skládání zkoušky pro přidělení amerického občanství soudci ukázat logické chyby v ústavě USA, díky kterým "by bylo možné, aby se někdo stal naprosto legálním způsobem diktátorem a nastolil fašistický režim".
December 27, 2021
While it would take a more mathematically sophisticated reader than yours truly to unpack the critical pages of this book that concern Gödel’s “Incompleteness Theorem,” the philosophical implication that he drew from his work is clear and wide-ranging: there are truths that are unprovable, that will always escape the grasp of mathematical rules. Quite beyond these issues, however, this book is a fascinating account of the remarkable group of mathematicians and other scientists, mostly Jewish, who gathered in Vienna during the 1920s and 30s. We all know what was soon to happen, and the author traces the consequences, which he calls the largest brain drain in world history, as so many of these scholars fled Austria and settled in the West, particularly America. Gödel was one of the more important members of the Vienna circle and later became a good friend of Albert Einstein, who held him in the highest esteem, at the Princeton Institute for Advanced Study. Just as one has a hard time imagining Thomas Mann and Arnold Schönberg living out their lives in Los Angeles, it is sometimes hard to imagine Gödel, depressive and increasingly paranoid, and other Austrian and German refugees finding refuge in what was at that time a very conservative New Jersey town. At any rate, this is an enjoyable and informative read on many levels, even if one doesn’t always get the math!
April 10, 2023
I am of a mixed opinion on this book. On the one hand, the descriptions of prewar Vienna, and especially the Vienna Circle and its members, were excellent. On the other hand, the author spent too much time contextualizing his subject, spending upwards of 40 pages on the history of the Hapsburg Empire and Austria-Hungary dating back to the mid 1700's. I found myself waiting for the author to justify the relevance and necessity of this exceptionally detailed backdrop, but in the end was not convinced that it added enough value. Similar attention was lavished on the history of the Institute for Advanced Study, which, while of more immediate relevance, seemed excessive as well. I think a stricter editor would have streamlined the book to its benefit. The actual biographical parts of the book were very engaging, although I still do not feel that I truly understand much of Gödel as an individual. I do not think this was due to a lack of thoroughness or skill on the author's part, but more likely a lack of source material.
April 16, 2025
A different take on the story of the Vienna Circle, this time by focussing on Kurt Gödel, the infuriatingly nerdy, razor-sharp and crystal-fragile logician/mathematician.
By limiting the focus to an often extremely dry, even unsympathetic, character, who was not known for his sociability, you're also limiting the sources of usable source material, and so quite a lot of space is devoted to scene-setting (e.g. the history and politics of late-era Habsburg Austria), which, rather than padding, I felt provided a useful context in which to understand the environment and influences on the man himself. Others might disagree!
Another trick which I appreciated was to provide only a cursory explanation of Gödel's major work within the main text, and to expand on this in an appendix. This kept the narrative flow, and allowed lowbrow dilletantes like myself to persuade themsleves that they had dug deep enough into the "meat" by skimming the extra text later. (It would have been a major flaw to have NOT included some technical detail, but this is definitely not an academic text!)
This is in many places a sad tale (encompassing Nazi takeover, mental illness, social alienation, etc.) but there are lighter episodes throughout. A high point, worth reading through most of the book to reach, is Gödel's interview for the US citizenship qualification, featuring Albert Einstein in a comic role.
By limiting the focus to an often extremely dry, even unsympathetic, character, who was not known for his sociability, you're also limiting the sources of usable source material, and so quite a lot of space is devoted to scene-setting (e.g. the history and politics of late-era Habsburg Austria), which, rather than padding, I felt provided a useful context in which to understand the environment and influences on the man himself. Others might disagree!
Another trick which I appreciated was to provide only a cursory explanation of Gödel's major work within the main text, and to expand on this in an appendix. This kept the narrative flow, and allowed lowbrow dilletantes like myself to persuade themsleves that they had dug deep enough into the "meat" by skimming the extra text later. (It would have been a major flaw to have NOT included some technical detail, but this is definitely not an academic text!)
This is in many places a sad tale (encompassing Nazi takeover, mental illness, social alienation, etc.) but there are lighter episodes throughout. A high point, worth reading through most of the book to reach, is Gödel's interview for the US citizenship qualification, featuring Albert Einstein in a comic role.
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