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My Brain Is Open: The Mathematical Journeys of Paul Erdos [Japanese Edition]
Physicist and science writer Bruce Schechter's biography of legendary Hungarian mathematician Paul Erdös is an engaging portrait, warm and intimate, bringing this strange, happy man to life. Schechter's focus is quite a bit tighter, and more traditionally biographical, than Paul Hoffman's in The Man Who Loved Only Numbers. Here, we get to see Erdös's brief childhood transform quickly into a carefree adolescence of solving difficult math problems with his circle of brilliant friends--uniquely encouraged by a country that valued the contributions of mathematics in a way that has never been equaled. Fleeing the Holocaust, Erdös never settled down, instead traveling from place to place, showing up on the doorsteps of other mathematicians with his few possessions and an open mind. During his career, Erdös published more papers than any other mathematician in history. Most of the papers were collaborations:
For Erdös, the mathematics that consumed most of his waking hours was not a solitary pursuit but a social activity. One of the great mathematical discoveries of the twentieth century was the simple equation that two heads are better than one.... That radical transformation of how mathematics is created is the result of many factors, not the least of which was the infectious example set by Erdös.
Schechter spoke with many of Erdös's collaborators to complete this biography, which reveals the odd mathematician as charming, opinionated, and completely dependent upon the kindness of others. Schechter not only tells his fascinating story, but introduces some intriguing mathematics problems (with easy-to-understand explanations) to show readers why Erdös loved the elegance of numbers more than anything else in the world. --Therese Littleton
Tankobon Hardcover
First published September 1, 1998
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October 23, 2016
It's probably fair to say that a large majority of the general public in the U. S. could not name a single important mathematician who was active in the period 1933 to 1996 (the years of Paul Erdős' adult life). A few people might think of Andrew Wiles, John von Neumann, or perhaps Kurt Gödel. It would be surprising if more than a percent or two could mention Paul Erdős or even recognize the name. Yet Erdős is probably one of the dozen or so most important mathematicians of that period. For instance, nobody in the history of the world published more new mathematical results (almost 1500), except for Leonhard Euler (who died in 1783).
Erdős created himself or was among the creators of a number of new mathematical specialties, including combinatorics, Ramsey theory, probabalistic number theory, and combinatorial geometry. He also made ground-breaking advances in the early stages of set theory and graph theory. And he added very substantially to classical number theory (one of Euler's specialties). In addition to his astonishing productivity, he remained active and prolific until he died at the age of 83 – something almost unheard of among mathematicians. Nevertheless he had little or no interest in many other branches of modern mathematics, such as topology, abstract algebra, or mathematical physics.
Schechter's book is very good at explaining in general terms what each of those mathematical topics are about and the contribution made by Erdős. Unlike most modern mathematics, the things that interested Erdős the most were "simple" things, like numbers and geometrical figures that are familiar to most people. So it's easy enough to understand most of what Erdős worked on. It would be nearly impossible, however, to explain to non-mathematicians the techniques by which the results were obtained. (After all, his results had eluded all earlier mathematicians.) And even mathematicians are mystified by the mental processes that led to the results.
Erdős was quite an unusual person in other respects as well. He never married or had any apparent sexual interests. During most of his adult life he had no permanent home and almost no possessions other than a couple of suitcases, some notebooks, and a few changes of clothes. He was almost perpetually on the go from one place to another after his welcome at one host's abode started to wear thin. And his memory was phenomenal – though only for details that were important to him, namely anything relevant to mathematics he cared about and his vast network of mathematical collaborators.
He co-authored papers with almost 500 other mathematicians, and personally discussed mathematics with hundreds of others. He generally knew the phone numbers and other personal details of most in his network. (Yet he was often unable to associate their names and details with their faces when he encountered them at meetings.) He was also able to recall technical details and publication information of thousands of mathematical papers, which may have been published decades previously. This fact probably helps explain his ability in many cases to solve new problems within minutes, because he could recall such a vast number of earlier results and techniques.
Schechter's biography is generally quite good. The author has a PhD in physics and is obviously conversant with the mathematics that interested his subject. There are just a few minor issues. Although Schechter never actually met Erdős, many personal anecdotes are reported. Those must have come from conversations with associates of Erdős or articles about him, but there's only a two-page "Note on Sources" instead of footnotes with specific details. There is a good bibliography, however.
The book is only about 200 pages, so it's a quick read. However, if it had been a little longer, it could have gone into somewhat more detail about Erdős' mathematics – such as set theory and probability theory. Another Erdős biography (The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth) was published about the same time, less than 2 years after the subject's death. (I've reviewed that one too.) So both biographers most likely wanted to get published as quickly as possible. There are clear signs of haste in both cases. In the present book there are few things that a proofreading should have caught, but only one more serious error: in Chapter 4 there are incorrect references to two of the graph diagrams.
All in all, this biography can be highly recommended for an overview of Erdős' mathematics, a fine portrait of a very unique and colorful individual, and the opportunity to gain a little understanding of the social process in which mathematics of the highest caliber is actually created.
Erdős created himself or was among the creators of a number of new mathematical specialties, including combinatorics, Ramsey theory, probabalistic number theory, and combinatorial geometry. He also made ground-breaking advances in the early stages of set theory and graph theory. And he added very substantially to classical number theory (one of Euler's specialties). In addition to his astonishing productivity, he remained active and prolific until he died at the age of 83 – something almost unheard of among mathematicians. Nevertheless he had little or no interest in many other branches of modern mathematics, such as topology, abstract algebra, or mathematical physics.
Schechter's book is very good at explaining in general terms what each of those mathematical topics are about and the contribution made by Erdős. Unlike most modern mathematics, the things that interested Erdős the most were "simple" things, like numbers and geometrical figures that are familiar to most people. So it's easy enough to understand most of what Erdős worked on. It would be nearly impossible, however, to explain to non-mathematicians the techniques by which the results were obtained. (After all, his results had eluded all earlier mathematicians.) And even mathematicians are mystified by the mental processes that led to the results.
Erdős was quite an unusual person in other respects as well. He never married or had any apparent sexual interests. During most of his adult life he had no permanent home and almost no possessions other than a couple of suitcases, some notebooks, and a few changes of clothes. He was almost perpetually on the go from one place to another after his welcome at one host's abode started to wear thin. And his memory was phenomenal – though only for details that were important to him, namely anything relevant to mathematics he cared about and his vast network of mathematical collaborators.
He co-authored papers with almost 500 other mathematicians, and personally discussed mathematics with hundreds of others. He generally knew the phone numbers and other personal details of most in his network. (Yet he was often unable to associate their names and details with their faces when he encountered them at meetings.) He was also able to recall technical details and publication information of thousands of mathematical papers, which may have been published decades previously. This fact probably helps explain his ability in many cases to solve new problems within minutes, because he could recall such a vast number of earlier results and techniques.
Schechter's biography is generally quite good. The author has a PhD in physics and is obviously conversant with the mathematics that interested his subject. There are just a few minor issues. Although Schechter never actually met Erdős, many personal anecdotes are reported. Those must have come from conversations with associates of Erdős or articles about him, but there's only a two-page "Note on Sources" instead of footnotes with specific details. There is a good bibliography, however.
The book is only about 200 pages, so it's a quick read. However, if it had been a little longer, it could have gone into somewhat more detail about Erdős' mathematics – such as set theory and probability theory. Another Erdős biography (The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth) was published about the same time, less than 2 years after the subject's death. (I've reviewed that one too.) So both biographers most likely wanted to get published as quickly as possible. There are clear signs of haste in both cases. In the present book there are few things that a proofreading should have caught, but only one more serious error: in Chapter 4 there are incorrect references to two of the graph diagrams.
All in all, this biography can be highly recommended for an overview of Erdős' mathematics, a fine portrait of a very unique and colorful individual, and the opportunity to gain a little understanding of the social process in which mathematics of the highest caliber is actually created.
March 29, 2011
Paul Erdős (pronounced air-dish) was a famous, eccentric and highly prolific mathematician who authored many hundreds of papers in collaboration with hundreds of other mathematicians. His name was unfamiliar to me until I read this xkcd cartoon, which makes an inside joke about Erdős Numbers, which are similar to links in the Six Degrees of Kevin Bacon game - they describe a mathematician's "collaborative distance" from Erdős.
This is a short book, and not so much a biography of Erdős as a collection of anecdotes about his interactions with the community of great 20th-century mathematicians. It's also full of descriptions of the mathematical concepts that fascinated Erdős, related in terms understandable to anyone with high school algebra. So this is a book for laymen, not mathematicians, who will be bored because they are probably already familiar with topics such as Pythagoras's proof that the square root of 2 is irrational, and the friendship theorem (or party problem), and Cantor's diagonal argument.
Not being a mathematician myself, I found the book informative and entertaining. I must admit, though, that I don't quite understand the endless fascination with prime numbers - how many there are, how far apart they are, how many even numbers must exit between them, how many integers in a certain range must be "relatively" prime, etc.
This is a short book, and not so much a biography of Erdős as a collection of anecdotes about his interactions with the community of great 20th-century mathematicians. It's also full of descriptions of the mathematical concepts that fascinated Erdős, related in terms understandable to anyone with high school algebra. So this is a book for laymen, not mathematicians, who will be bored because they are probably already familiar with topics such as Pythagoras's proof that the square root of 2 is irrational, and the friendship theorem (or party problem), and Cantor's diagonal argument.
Not being a mathematician myself, I found the book informative and entertaining. I must admit, though, that I don't quite understand the endless fascination with prime numbers - how many there are, how far apart they are, how many even numbers must exit between them, how many integers in a certain range must be "relatively" prime, etc.
April 4, 2025
writing my term paper on erdős. enjoyed. good info on his travel and immigration which is what i’m focusing on so that’s helpful. better narrative story than hoffman’s
April 6, 2015
In Hungary, in the decades after 1900 and before World War II, existed an intense "math scene" in which young people, Jews mostly, spent long hours of excited energy arguing and devising proofs for mathematical problems.
They would meet at the city park in Budapest, many of them proteges of some of the great math teachers in the city at the time.
They competed with, and fed off, each other, much like the bebop musicians of Harlem did in the 1940s as they were revolutionizing jazz.
The city had a mathematical journal prodding this intensity by publishing problems every month, along with the best proofs of previous months' problems. It was apparently read by kids in Hungary the way American kids read comic books today.
All this was destroyed by WWII and then communism. But the numbers of titanic mathematical minds to emerge from Hungary during those years was probably unparalleled in the history of the world. They would change technology, industry and more with their work.
I don't know much about mathematics, but I'm fascinated by the people who do it at the highest levels. Paul Erdos was one of these.
This book is his life story, beginning with his years as a child prodigy growing up in the mathematical hotbed that was Budapest then.
As an adult, he literally had no home, but lived from a suitcase - which contained a few articles of clothing, and more articles about mathematics - a wandering Jew, obsessed with proofs, and living from the generosity of mathematicians with whom he stayed as he traveled the world for decades.
He wrote more than 1500 papers. This is the kind of book where what you takes from it, unless you're a mathematician, is not specifics, but a general feel, a vibe - in this case, about how great minds create.
Erdos was, according to Schechter, among the first to turn mathematics into a communal, and community, enterprise. To that point, most mathematicians labored in solitary confinement with their theorems. Most of Erdos's were, instead, collaborations with others.
I'm rereading this book, which I discovered and read in the late 1990s. It comes at a time when I'm about to publish a book of my own - this about America's addiction to painkillers and heroin, the exquisite expression of narcissism, isolation, individualism, and self-centeredness.
Therefore, I may be searching, more than usually, for cases in which community and collaboration create great things.
They would meet at the city park in Budapest, many of them proteges of some of the great math teachers in the city at the time.
They competed with, and fed off, each other, much like the bebop musicians of Harlem did in the 1940s as they were revolutionizing jazz.
The city had a mathematical journal prodding this intensity by publishing problems every month, along with the best proofs of previous months' problems. It was apparently read by kids in Hungary the way American kids read comic books today.
All this was destroyed by WWII and then communism. But the numbers of titanic mathematical minds to emerge from Hungary during those years was probably unparalleled in the history of the world. They would change technology, industry and more with their work.
I don't know much about mathematics, but I'm fascinated by the people who do it at the highest levels. Paul Erdos was one of these.
This book is his life story, beginning with his years as a child prodigy growing up in the mathematical hotbed that was Budapest then.
As an adult, he literally had no home, but lived from a suitcase - which contained a few articles of clothing, and more articles about mathematics - a wandering Jew, obsessed with proofs, and living from the generosity of mathematicians with whom he stayed as he traveled the world for decades.
He wrote more than 1500 papers. This is the kind of book where what you takes from it, unless you're a mathematician, is not specifics, but a general feel, a vibe - in this case, about how great minds create.
Erdos was, according to Schechter, among the first to turn mathematics into a communal, and community, enterprise. To that point, most mathematicians labored in solitary confinement with their theorems. Most of Erdos's were, instead, collaborations with others.
I'm rereading this book, which I discovered and read in the late 1990s. It comes at a time when I'm about to publish a book of my own - this about America's addiction to painkillers and heroin, the exquisite expression of narcissism, isolation, individualism, and self-centeredness.
Therefore, I may be searching, more than usually, for cases in which community and collaboration create great things.
June 17, 2011
I started reading this when my husband decided to go back to school for first a masters and then a PhD in mathematics. He's now a mathematics professor.
July 19, 2014
My Brain Is Open to The mathematical journeys of Paul Erdos
"The meaning of life, Erdos often said, was to prove and conjecture. Proof and conjecture are the tools with which mathematicians explore the Platonic universe of pure form, a universe that to many of them is as real as the universe in which they must reluctantly make their homes and livings, and far more beautiful."
In the world of mathematics, Erdos was an icon. His stature and influence on mathematicians and on the mathematical world of the last century was primary. The author, Bruce Schechter, has made a well researched and intriguing foray into the life and work of this mathematical prodigy. Taking the Odyssean meme of a journey, Schechter, traces the major themes of Erdos' mathematical journey beginning with his confounding discovery as a toddler of the existence of negative numbers through to his obsession with the properties and functionality of number theory, prime numbers, combinatorics, set theory, polynomials, and so on. Erdos' expansive range of mathematical expertise and proficiency in publishing papers was epic. Schechter poignantly states "Erdos was everywhere. He was the nearest thing to an ergodic particle (one that eventually visits all physically possible states) that a human could be."
Erdos followed a different approach to problem solving, focusing on specific problems, confident that as he solved them the general theory would slowly be revealed. His study of Prime Numbers, the Queen of Mathematics, led to some beautiful proofs concerning the distribution and density of primes in large numbers. Prime numbers possess unique properties including self generation, self-sufficiency and indivisibility that is a number that cannot be divided by any number other than by itself. Erdos was fascinated by the patterned disorderliness of prime numbers. That is, primes are spread so thinly among large numbers compared to primary numbers. Erdos demonstrated that between any number greater than 7 and its double there will always be at least two primes.
This book finds the right balance between exposing personal insights and exploring mathematical theorems to explain the genius behind the work. My Brain Is Open is filled with quips and quirks about and by Erdos such as his charming reference to children as Epsillons (mathematical term for small quantities) or "A Mathematician is a machine for turning coffee into theorems." Erdos is portrayed here as an unique individual with an extraordinary gift to mathematize. He was a wayfarer in Math's vanguard.
"The meaning of life, Erdos often said, was to prove and conjecture. Proof and conjecture are the tools with which mathematicians explore the Platonic universe of pure form, a universe that to many of them is as real as the universe in which they must reluctantly make their homes and livings, and far more beautiful."
In the world of mathematics, Erdos was an icon. His stature and influence on mathematicians and on the mathematical world of the last century was primary. The author, Bruce Schechter, has made a well researched and intriguing foray into the life and work of this mathematical prodigy. Taking the Odyssean meme of a journey, Schechter, traces the major themes of Erdos' mathematical journey beginning with his confounding discovery as a toddler of the existence of negative numbers through to his obsession with the properties and functionality of number theory, prime numbers, combinatorics, set theory, polynomials, and so on. Erdos' expansive range of mathematical expertise and proficiency in publishing papers was epic. Schechter poignantly states "Erdos was everywhere. He was the nearest thing to an ergodic particle (one that eventually visits all physically possible states) that a human could be."
Erdos followed a different approach to problem solving, focusing on specific problems, confident that as he solved them the general theory would slowly be revealed. His study of Prime Numbers, the Queen of Mathematics, led to some beautiful proofs concerning the distribution and density of primes in large numbers. Prime numbers possess unique properties including self generation, self-sufficiency and indivisibility that is a number that cannot be divided by any number other than by itself. Erdos was fascinated by the patterned disorderliness of prime numbers. That is, primes are spread so thinly among large numbers compared to primary numbers. Erdos demonstrated that between any number greater than 7 and its double there will always be at least two primes.
This book finds the right balance between exposing personal insights and exploring mathematical theorems to explain the genius behind the work. My Brain Is Open is filled with quips and quirks about and by Erdos such as his charming reference to children as Epsillons (mathematical term for small quantities) or "A Mathematician is a machine for turning coffee into theorems." Erdos is portrayed here as an unique individual with an extraordinary gift to mathematize. He was a wayfarer in Math's vanguard.
May 1, 2017
3.5 stars truthfully. While this is a short book on the long and laborious life of the eccentric Paul Erdős, it does highlight his imaginative mind and his love of mathematics. It begins with the familiar account of a child (epsilon) prodigy who has an appetite for mathematics and their extreme calculating abilities. His love for mathematics began early and never ceases throughout his life.
Paul had the most collaborative history of any mathematician up to that point. The book highlights his many collaborations and only briefly outlines some of the rudimentary problems that he devoted his time to. A reader of Erdős looking for a more detailed account of his mathematics should seek out the multi volume collection of works published shortly after his death in 1996. This book is for the reader who is seeking a brief account of his life without being to technical. I would have liked a more rigorous book, but that's me.
In short, if you want to read about a man who traveled the world, never staying in one place for work or friends or family and is enamored with the pursuit of mathematical truth, then I can recommend this book. I can also recommend the more personal documentary, N is a Number which showcases his eccentric way of living. Erdős was the most prolific of any mathematician and one of the most free human beings the sciences had ever seen; an absolute rarity the world was glad to have.
Paul had the most collaborative history of any mathematician up to that point. The book highlights his many collaborations and only briefly outlines some of the rudimentary problems that he devoted his time to. A reader of Erdős looking for a more detailed account of his mathematics should seek out the multi volume collection of works published shortly after his death in 1996. This book is for the reader who is seeking a brief account of his life without being to technical. I would have liked a more rigorous book, but that's me.
In short, if you want to read about a man who traveled the world, never staying in one place for work or friends or family and is enamored with the pursuit of mathematical truth, then I can recommend this book. I can also recommend the more personal documentary, N is a Number which showcases his eccentric way of living. Erdős was the most prolific of any mathematician and one of the most free human beings the sciences had ever seen; an absolute rarity the world was glad to have.
December 23, 2015
A thoroughly delightful biography of a true eccentric genius. Erdos traveled the world (almost never in the same bed for a week in a row), staying with friends and doing math.
August 7, 2024
Αξίζει να διαβάσετε όλοι για την ζωή αυτού του ανθρώπου!!!
Την ζωή του Ερντος αξίζει να την έχει κατά νου ο καθένας, άσχετα με το αν είναι/θέλει να γίνει μαθηματικός ή όχι, τα μαθηματικά που αναφέρονται στο βιβλίο είναι κατανοητά για τον καθένα και ο,τι χρειάζεται το οποίο είναι εκτός σχολικής ύλης επεξηγείται. Το ότι έχει ιστορικές αναδρομές για κοινωνικά - πολιτικά ζητήματα σίγουρα προκύπτει από το γεγονός ότι ο Ερντος είχε έντονες κοινωνικοπολιτικές ευαισθησίες και κάνει την βιογραφία του πιο ολοκληρωμένη.
Γέλασα σε πολλά σημεία του βιβλίου, κυρίως διότι ο Ερντος ήταν ένας άνθρωπος με απίστευτο χιούμορ και αυτό φαίνεται από τις αφηγήσεις του συγγραφέα.
Αξίζει να σημειωθεί ότι πολλά από αυτά που αναφέρονται στο βιβλίο έχουν γίνει γνωστά από συζητήσεις του συγγραφέα με γνωστούς ή φίλους του Ερντος, μετά τον θάνατο του.
<<Το μυαλό μου είναι ανοιχτό>>
Δεν θα μπορούσε να υπάρξει πιο όμορφος τίτλος για την βιογραφία αυτού του ανθρώπου.
Την ζωή του Ερντος αξίζει να την έχει κατά νου ο καθένας, άσχετα με το αν είναι/θέλει να γίνει μαθηματικός ή όχι, τα μαθηματικά που αναφέρονται στο βιβλίο είναι κατανοητά για τον καθένα και ο,τι χρειάζεται το οποίο είναι εκτός σχολικής ύλης επεξηγείται. Το ότι έχει ιστορικές αναδρομές για κοινωνικά - πολιτικά ζητήματα σίγουρα προκύπτει από το γεγονός ότι ο Ερντος είχε έντονες κοινωνικοπολιτικές ευαισθησίες και κάνει την βιογραφία του πιο ολοκληρωμένη.
Γέλασα σε πολλά σημεία του βιβλίου, κυρίως διότι ο Ερντος ήταν ένας άνθρωπος με απίστευτο χιούμορ και αυτό φαίνεται από τις αφηγήσεις του συγγραφέα.
Αξίζει να σημειωθεί ότι πολλά από αυτά που αναφέρονται στο βιβλίο έχουν γίνει γνωστά από συζητήσεις του συγγραφέα με γνωστούς ή φίλους του Ερντος, μετά τον θάνατο του.
<<Το μυαλό μου είναι ανοιχτό>>
Δεν θα μπορούσε να υπάρξει πιο όμορφος τίτλος για την βιογραφία αυτού του ανθρώπου.
April 5, 2024
(first draft, it's I think repetitive, but I just want to set it all out, whether or not I return to make it more readable)
Erdős is a hero of mine, and this review is from the perspective of a fan, and I cannot guarantee its applicability to the general reader.
In comparison with the Hoffman book, this one is more chronological, presents a more 'realistic' portrait of Erdős, and spends more time explaining the basics of the math on which Erdos worked. I am not so confident in this, but am confident that this is the impression you would be left with if you read Hoffman first and then this two years later, and watched the documentary at a few different points....
Both books (and the documentary) are essentially piles of anectdotes and documentation of the Erdős lore, which is anyway what I signed up for, and so I do not complain of redundancy. (They differ in their explanations for why he couldn't stay at Princeton's IAS.) But there is only so much lore, and I already had heard most of it. Hoffman seems more concerned with what, in Shechter's telling, might be called the 'late' Erdős, the span of time during which is mother was traveling with him and after she died, and during which Ron Graham seems to have taken over managing Erdős' affairs. I say this portrait is more 'realistic' because it doesn't spend as much time on his incompetencies--the 'buttered toast' anectdote is downplayed, and S. doesn't mention the idea that he couldn't make any food for himself; the 'grapefruit' anectdote isn't even included, although a reference to 'dripping tomato juice' is made--and there is less emphasis on how everyone took care of him, although this is mentioned in the last chapter. I claim that the H. book is more about the late Erdős because there were all these things that felt shoehorned in at the end of the S. book that felt more central in H., and one gets the idea that S. reads H. at that point in working on the manuscript.... More realistic also because the idea that Erdős feigned incompetency is suggested, but not lingered on. The actual substance of the math, popularized as it was, bored me. Much of the book was very basic, in its explanations of mathematics and the math world and so on, which sometimes made it feel lazy or unresearched (the bibliography is bad too), but the writing was competent and I think the explanation for the boilerplate was that that's what the book was trying to be.
But of course, what of his inner life? This shall remain mysterious. Erdős was so happy, and he lived the life of an eccentric so effortlessly, but how? He was weirdly asexual; the documentary's claim that he "can't stand sexual pleasure" may be true, he could have had some congenital deformity, but it seems more likely to me that he had a fear of sexuality, and never needed to overcome it, being free of the pressure to conform or in fact almost any restraint at all. (That he had Asperberger's is obvious; he's described as flapping his arms and completely absentminded, at times in excruciatingly recognizable ways.) The life of an itinerant--as his obituary called him, a "wayfarer on math's vanguard"--is so, so appealing to me; how could he live it? For one, his area was math, which has a number of distinct advantages:
1) That the work is real, difficult, and intellectual is obvious to outsiders, and the results are concrete. Without these, his genius wouldn't've been legible to outsiders, and so his eccentricty would've been less well tolerated. Seeming like a genius is key. (And here, might even his thick accent have helped?)
2) Also because his area was pure mathematics, he could work anywhere, with just his mind--he didn't need a lab, or to spend time collecting data, etc.
3) He was a genius--and even more so, I think, than he's remembered as, or at least that I appreciated. Erdős worked so much faster than everyone else, that he could actually benefit them when he arrived.
I also think Erdős was so well-received because of his asexuality... If he had been a world-traveling genius who loved women, he would not only have wasted a great deal of time in pursuit of them, but would have made enemies, contemporary or retrospective. He also would have had more aggression, I think; as it stands, he was kind and beloved, he was wholesome. And of course, womanizing would make it much harder for him to stay with these random mathematicians for weeks at a time.... And again because the area was math, there were young people in whom he could take an interest; the only other areas where you might find such precocity would be music and chess. And they wouldn't work for other reasons: The former, especially now, would be less esteemed, less provable to outsiders; the latter doesn't benefit from collaboration per se, and its genius is relative and adversarial, rather than collaborative and aimed at solving discrete problem. Really neither--almost nothing, it seems--has quite the same structure, where the goal is publishing papers, the contents of which come straight from the mind.
But there is something so attractive about the life of Erdős, a life devoted to extreme productivity, with no attachments but two half-empty suitcases, especially, spent traveling and seeing other experts, talking with them. The Hoffman book (and the article it's based on) is called The Man Who Loved Only Numbers, which isn't right--Erdős loved people, especially his mother. But his productivity wasn't about money or success or status--he had a saintly disinterst in those things. It wasn't a tense or striving productivity; it was happy and oriented toward truth and beauty, The Book, in his parlance. This is a kind of saintliness that I think excludes me from realizing what I find so inspiring in him: he was devoid of the impulse towards sex and status and rivalry and therefore, ultimately, aggression. Like Socrates (and probably some saints), he didn't achieve this morality, but was born with it.
Why is his life so appealing? Its itinerancy, the involvement of others, being beloved, its total dedication to knowledge, and especially the parts of knowledge that are beautiful. But also because it worked out--that his life was completely free of the constraints of normal existence. People really did take care of him and allowed him to focus on what mattered. Toward the end of his life, he refused to listen to the doctors WRT his pacemaker surgery; they said it was like restraining a wild animal. Well, he'd lived free from restraint his whole life, and in service of something more important, and it wouldn't start then. It's a fantasy, and a fantasy which was reliant on asexuality; an unconstrained life that involved a wife or children would result in his abandonment of them, and cast a shadow over the whole thing.
Schematic: I'd here like to say something about how E was so happy, and that often with mathematicians--of course exaggerated in the collected tales of a beloved eccentric genius--you get a very socially simple account of human life, even as the simple narratives can't possibly fit. Like Tracy Austin, E.'s was an incredible life, but no one will ever know quite what it was like, including, probably, E. himself. S. discusses his mother's death, and here gets close. There is no attempt at a psychological portrait of the interior. Some of that, again like Tracy Austin, reflects that there probably was no such interior; some that there was, but it was never noticed, even by E.; some, simply because we do not have the evidence for it. Or the suggestion that E. played up his incompetence. I will develop this if I have the time.
Erdős was unbelievably energetic; energy is so important, yet rarely discussed (it is like intelligence in this respect). Is it ignored, or genuinely unnoticed? Regardless, both have a kind of incontestible innateness, at least at the extremes. Some silent process works everything out before they become conscious thoughts, and is their real determiner. The ping pong story emphasizes this.
It is fascinating, unbelievable, what was in the air among in Budapest among Hungarian Jews in the beginning of the 20c. "
Erdős is a hero of mine, and this review is from the perspective of a fan, and I cannot guarantee its applicability to the general reader.
In comparison with the Hoffman book, this one is more chronological, presents a more 'realistic' portrait of Erdős, and spends more time explaining the basics of the math on which Erdos worked. I am not so confident in this, but am confident that this is the impression you would be left with if you read Hoffman first and then this two years later, and watched the documentary at a few different points....
Both books (and the documentary) are essentially piles of anectdotes and documentation of the Erdős lore, which is anyway what I signed up for, and so I do not complain of redundancy. (They differ in their explanations for why he couldn't stay at Princeton's IAS.) But there is only so much lore, and I already had heard most of it. Hoffman seems more concerned with what, in Shechter's telling, might be called the 'late' Erdős, the span of time during which is mother was traveling with him and after she died, and during which Ron Graham seems to have taken over managing Erdős' affairs. I say this portrait is more 'realistic' because it doesn't spend as much time on his incompetencies--the 'buttered toast' anectdote is downplayed, and S. doesn't mention the idea that he couldn't make any food for himself; the 'grapefruit' anectdote isn't even included, although a reference to 'dripping tomato juice' is made--and there is less emphasis on how everyone took care of him, although this is mentioned in the last chapter. I claim that the H. book is more about the late Erdős because there were all these things that felt shoehorned in at the end of the S. book that felt more central in H., and one gets the idea that S. reads H. at that point in working on the manuscript.... More realistic also because the idea that Erdős feigned incompetency is suggested, but not lingered on. The actual substance of the math, popularized as it was, bored me. Much of the book was very basic, in its explanations of mathematics and the math world and so on, which sometimes made it feel lazy or unresearched (the bibliography is bad too), but the writing was competent and I think the explanation for the boilerplate was that that's what the book was trying to be.
But of course, what of his inner life? This shall remain mysterious. Erdős was so happy, and he lived the life of an eccentric so effortlessly, but how? He was weirdly asexual; the documentary's claim that he "can't stand sexual pleasure" may be true, he could have had some congenital deformity, but it seems more likely to me that he had a fear of sexuality, and never needed to overcome it, being free of the pressure to conform or in fact almost any restraint at all. (That he had Asperberger's is obvious; he's described as flapping his arms and completely absentminded, at times in excruciatingly recognizable ways.) The life of an itinerant--as his obituary called him, a "wayfarer on math's vanguard"--is so, so appealing to me; how could he live it? For one, his area was math, which has a number of distinct advantages:
1) That the work is real, difficult, and intellectual is obvious to outsiders, and the results are concrete. Without these, his genius wouldn't've been legible to outsiders, and so his eccentricty would've been less well tolerated. Seeming like a genius is key. (And here, might even his thick accent have helped?)
2) Also because his area was pure mathematics, he could work anywhere, with just his mind--he didn't need a lab, or to spend time collecting data, etc.
3) He was a genius--and even more so, I think, than he's remembered as, or at least that I appreciated. Erdős worked so much faster than everyone else, that he could actually benefit them when he arrived.
I also think Erdős was so well-received because of his asexuality... If he had been a world-traveling genius who loved women, he would not only have wasted a great deal of time in pursuit of them, but would have made enemies, contemporary or retrospective. He also would have had more aggression, I think; as it stands, he was kind and beloved, he was wholesome. And of course, womanizing would make it much harder for him to stay with these random mathematicians for weeks at a time.... And again because the area was math, there were young people in whom he could take an interest; the only other areas where you might find such precocity would be music and chess. And they wouldn't work for other reasons: The former, especially now, would be less esteemed, less provable to outsiders; the latter doesn't benefit from collaboration per se, and its genius is relative and adversarial, rather than collaborative and aimed at solving discrete problem. Really neither--almost nothing, it seems--has quite the same structure, where the goal is publishing papers, the contents of which come straight from the mind.
But there is something so attractive about the life of Erdős, a life devoted to extreme productivity, with no attachments but two half-empty suitcases, especially, spent traveling and seeing other experts, talking with them. The Hoffman book (and the article it's based on) is called The Man Who Loved Only Numbers, which isn't right--Erdős loved people, especially his mother. But his productivity wasn't about money or success or status--he had a saintly disinterst in those things. It wasn't a tense or striving productivity; it was happy and oriented toward truth and beauty, The Book, in his parlance. This is a kind of saintliness that I think excludes me from realizing what I find so inspiring in him: he was devoid of the impulse towards sex and status and rivalry and therefore, ultimately, aggression. Like Socrates (and probably some saints), he didn't achieve this morality, but was born with it.
Why is his life so appealing? Its itinerancy, the involvement of others, being beloved, its total dedication to knowledge, and especially the parts of knowledge that are beautiful. But also because it worked out--that his life was completely free of the constraints of normal existence. People really did take care of him and allowed him to focus on what mattered. Toward the end of his life, he refused to listen to the doctors WRT his pacemaker surgery; they said it was like restraining a wild animal. Well, he'd lived free from restraint his whole life, and in service of something more important, and it wouldn't start then. It's a fantasy, and a fantasy which was reliant on asexuality; an unconstrained life that involved a wife or children would result in his abandonment of them, and cast a shadow over the whole thing.
Schematic: I'd here like to say something about how E was so happy, and that often with mathematicians--of course exaggerated in the collected tales of a beloved eccentric genius--you get a very socially simple account of human life, even as the simple narratives can't possibly fit. Like Tracy Austin, E.'s was an incredible life, but no one will ever know quite what it was like, including, probably, E. himself. S. discusses his mother's death, and here gets close. There is no attempt at a psychological portrait of the interior. Some of that, again like Tracy Austin, reflects that there probably was no such interior; some that there was, but it was never noticed, even by E.; some, simply because we do not have the evidence for it. Or the suggestion that E. played up his incompetence. I will develop this if I have the time.
Erdős was unbelievably energetic; energy is so important, yet rarely discussed (it is like intelligence in this respect). Is it ignored, or genuinely unnoticed? Regardless, both have a kind of incontestible innateness, at least at the extremes. Some silent process works everything out before they become conscious thoughts, and is their real determiner. The ping pong story emphasizes this.
It is fascinating, unbelievable, what was in the air among in Budapest among Hungarian Jews in the beginning of the 20c. "
October 23, 2011
I'm a little bit Erdos obsessed at the moment, so I came to this book already familiar with most of his extraordinary story. I previously read, and was blown away by, The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth, but I have to agree with others that this is the better biography. Schechter maintains the focus mores strongly on Erdos than Hoffman does, opting to delve farther into Erdos's work than the (more accessible) work of other more famous mathematicians. Schechter's writing is concise and to the point, where Hoffman's flourishes tangentially away from Erdos.
Hoffman wrote a better book for laypeople, as an overarching exploration of mathematics; Schechter wrote a more accurate depiction of Erdos as a human being and as a mathematician.
Comparisons aside, I really enjoyed this book. It gave me a stronger grasp of Erdos's work and a more rounded view of his life. It becomes incredibly clear that he did not only love numbers, and that his entire life was an admirable pursuit of a better world and a better understanding of it. He is a consummate inspiration to any scientist, anywhere.
Hoffman wrote a better book for laypeople, as an overarching exploration of mathematics; Schechter wrote a more accurate depiction of Erdos as a human being and as a mathematician.
Comparisons aside, I really enjoyed this book. It gave me a stronger grasp of Erdos's work and a more rounded view of his life. It becomes incredibly clear that he did not only love numbers, and that his entire life was an admirable pursuit of a better world and a better understanding of it. He is a consummate inspiration to any scientist, anywhere.
May 31, 2015
I studied mathematics in my undergraduate years and still like it at heart. This book is a collection of the famous mathematician Paul Erdos' life, characters, achievements and especially his approach to share insights and conjectures with rising or renowned mathematicians. This often resulted in the collabration with the genius a written paper and subsequently spark off the trend in the mathematics world to publish papers not just solo but in collabration among mathematicians.
The book was written with simple enough maths background requirments for readers to appreciate Erdos' talents via proofs of various examples and explanations, which spans over the different kinds mathematics Erdos was working on (though his prime interest have been in Number Theory). His abilities and ideas also led to some of the mathematical branches we see today ... Ramsey theory, combinatorial geometry, extremal graph theory, random graph theory, probabilistic number theory etc. Some of these have been used extensively nowadays, especially in computer and communication networks implemenetation.
I especially like the book which refers back all the key mathematicians, their work and theorems etc during period of Erods (1913 - 1996).
The book was written with simple enough maths background requirments for readers to appreciate Erdos' talents via proofs of various examples and explanations, which spans over the different kinds mathematics Erdos was working on (though his prime interest have been in Number Theory). His abilities and ideas also led to some of the mathematical branches we see today ... Ramsey theory, combinatorial geometry, extremal graph theory, random graph theory, probabilistic number theory etc. Some of these have been used extensively nowadays, especially in computer and communication networks implemenetation.
I especially like the book which refers back all the key mathematicians, their work and theorems etc during period of Erods (1913 - 1996).
September 1, 2012
This is a quite short work. A strong sense of the character of Paul Erdos is given, without providing exhaustive details about his work. Biographical accounts are leavened with well known math history chestnuts, such as how Gauss summed the numbers from 1 to 100 as a child. The math is accessible to the non expert, and touches on areas such as the Prime Number Theorem, graph theory and probability.
The book often references the documentary about Erdos, N is a Number, which runs under an hour and can be found on youtube. At times I wondered why I was bothering to read the book when I could just watch the video it was referencing.
For the casual reader interested in math this book may be satisfying, but mathematicians and those who already know about Erdos will want more. By the way, I'm in the first camp; I was quite interested to learn about this wandering mendicant of math and the rich Hungarian tradition of academia he came from. As a side note, I should mention that the book had nice thick pages.
The book often references the documentary about Erdos, N is a Number, which runs under an hour and can be found on youtube. At times I wondered why I was bothering to read the book when I could just watch the video it was referencing.
For the casual reader interested in math this book may be satisfying, but mathematicians and those who already know about Erdos will want more. By the way, I'm in the first camp; I was quite interested to learn about this wandering mendicant of math and the rich Hungarian tradition of academia he came from. As a side note, I should mention that the book had nice thick pages.
December 31, 2012
This is a well-written biography of Paul Erdös, one of the greatest and most productive mathematicians of the twentieth century -- author of some 1,500 articles. Schechter portrays him as a profoundly sociable scholar who pioneered collaborative papers in mathematics, some written with teenage prodigies. Yet he was also a very unusual person, hyperactive as a child and with a horror of physical contact as an adult. Erdös Numbers have become a commonplace among mathematicians: co-authors of Erdös's score 1, co-authors of those co-authors 2, etc. Schechter makes everything very clear, combining moving tales of Hitlerian, Stalinist and McCarthyite oppression with many humorous and affectionate observations.
April 22, 2011
Paul Erdos was a remarkable mathematician not only for his prodigious ability but also for his single-minded devotion and his uncanny knack for collaboration. He arranged his life so as to maximize "proof and conjecture," even to the point of being homeless for much of his career. He lived off lecture honoraria and the hospitality of other mathematicians, who typically got to coauthor a paper with him in return. Erdos skillfully found ideas that were perfectly placed to spur collaborators of all ability levels to new insights. My Brain Is Open is a warm and occasionally even inspiring account of his life.
August 6, 2015
It's always amazing to me how many relatively unknown people have had profound effects upon society and the way we live today. Paul Erdős is one of those people, and this book helps to explain him, his life, and contributions. Erdős may have been a bit eccentric, but in Schechter's hands, he comes across as a fascinating man who truly loved mathematics, learning, and collaboration. If I was in charge, drug-abusing athletes, Paris Hilton, and the Kardashians would not be lauded as celebrities; instead we would celebrate Paul Erdős, Claude Shannon, Alan Turing, Karl Landsteiner, and Joseph Lister. This book is an interesting read about a very interesting human being.
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February 6, 2015In this interesting book about an eccentric mathematician Paul Erdos is a good story based biography about his life. Born in Hungary during the war had a rough childhood but lived with the constant war going on outside his house. Due to tubercolosis his two sisters died and his parents want into depression. Since he did not go to school because his parents were overprotective His dad taught him everything he knew about math during his young years. The middle of the book is very boring because rather than carrying his story on it describes his work is exciting until some point. If you are considering reading this book do realize that you have to go in with strong concepts.
July 29, 2014
This book introduced me to Paul Erdos more than a decade ago. Actually, I can say that this book made me like to read biographies in general. It is written in very lively tone. Very entertaining story about the legendary Paul Erdos, his 19 hours of working/day, his movement among conferences (He actually didn't have a home), and his continuous quest for proving theorems "from the book". If you like mathematics, especially number theory, then this book is a great source of inspiration. If you like to read about the eccentric life of a mathematical prodigy then this book is also for you.
December 18, 2012
A well-narrated story of Paul Erdos, one of the most prominent mathematicians of the 20th century, along with a brief history of number theories. The proofs and conjectures are the gems of this book, but the fact that only the simplest ones are explained at length may disappoint some math-oriented minds. Other than that, it is a fun and relaxing read on the beauty of numbers and the great personalities behind the discovery of such beauty.
July 9, 2018
A highly enjoyable look into the live of Paul Erdos. I had already heard about him in books like Prime obsession and Music of the Primes, but then primarily in the context of the disagreement with Atle Selberg. This books provides more information about the genius of Erdos and the way he worked and collaborated. The disagreement with Selberg is nicely handled in the book providing probably a well balanced view. Would love to have his lifestyle, if only I could afford it.
May 24, 2021
Picked it up at the library at my workplace. I am still a fan of reading physical (as opposed to electronic) books. The introduction mentions, among other things, that the Erdos (read 'airdish') has authored 1500 papers, his love for India and his itinerant lifestyle. And that was enough to get me to pick it up.
March 24, 2014
This is a fascinating and engaging biography of a true mathematical genius, Paul Erdos. I loved the anecdotes, the vivid portrait of a vital math community. While I didn't always "get" the math, I appreciated the glimpse into its rich complexities. Erdos was a remarkable individual, in so many ways.
June 16, 2010
Mainly a catalogue of anecdotes about an influencial genius who was additionally a truly humble and generous man. A sensible and balanced amount of mathematical content for a book of this nature.
Not in the same league as, say, "A Beautiful Mind" (about the mathematician John Nash).
Not in the same league as, say, "A Beautiful Mind" (about the mathematician John Nash).
July 22, 2010
I found it interesting to read about Paul Erdos. He's quite the personality! Sometimes when the author would get into all the math, it was too much thinking for me. And I have a relatively extensive background in math. So for someone unsure of their math, be prepared to skip some parts.
March 26, 2012
Engaging character. The author does a good job of showing the genius and the emotion of this brilliant mathematician. It is a very engaging read and only bogs down once or twice. I really enjoyed learning about prime numbers and the many obsessions people have with them.
August 6, 2011
a great book about an amazing mathematician that i'd never heard of. he was as brilliant as he was eccentric. i'm not big on biographies, but this one was really entertaining with great anecdotes and easy-to-understand explanations
June 2, 2012
A surprisingly great read. Erdos was truly eccentric, but a great human being. I never realized he even existed until this book unfolded his life story to me. If you love math, and interesting people who spend their lives entangled with math's enigmatic charms, this is a book for you.
September 12, 2007
Erdos is pronounced something like ' air - dish '
February 12, 2008
Those anecdotes about this great mathematician are intriguing and wonderfully inspiring. He's also one of my beloved mentors. By the way, my Erdo's number's beyond 5.
November 13, 2009
the story of a great mathematician, very well narrated.
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