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Hilbert
Now in new trade paper editions, these classic biographies of two of the greatest 20th Century mathematicians are being released under the Copernicus imprint. These noteworthy accounts of the lives of David Hilbert and Richard Courant are closely related: Courant's story is, in many ways, seen as the sequel to the story of Hilbert. Originally published to great acclaim, both books explore the dramatic scientific history expressed in the lives of these two great scientists and described in the lively, nontechnical writing style of Contance Reid.
272 pages, Paperback
First published January 1, 1970
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Displaying 1 - 23 of 23 reviews
January 29, 2019
A wonderful book and a sensitive portrait of one of the greatest and most versatile mathematicians in history who was also a great human being. The book is as much a paean to the romantic mathematical life as anything else. From his perch in Göttingen, Hilbert took German mathematics to great heights until it was brought crashing down by politics and Nazism. His finest hour came in World War 1 when he and Einstein refused to sign a shameful, jingoistic manifesto claiming Germany as the victim rather than the instigator of aggression; both Einstein and Hilbert were vilified as traitors for this.
In 1900 Hilbert set out 23 unsolved problems that would keep mathematicians busy for the next hundred years. He was obsessed with the formalization of all of math and physics, a dream that was shattered in 1931 by Kurt Gödel through his incompleteness theorems. This book again raises the question of how extreme intellectual achievement and extreme militarism can co-exist in the same country.
In 1900 Hilbert set out 23 unsolved problems that would keep mathematicians busy for the next hundred years. He was obsessed with the formalization of all of math and physics, a dream that was shattered in 1931 by Kurt Gödel through his incompleteness theorems. This book again raises the question of how extreme intellectual achievement and extreme militarism can co-exist in the same country.
December 3, 2007
Worth it for the Hilbert picture where he looks just like the Black Mage from the original Final Fantasy.
August 22, 2020
Truly outstanding! As probably many others, I first wondered whether a non-mathematician would be able to retell the mathematical aspects of Hilbert's life. Just a few pages in, however, I was pleasantly surprised. I would not have guessed that the author was not a mathematician.
Hilbert's life is truly fascinating and I find it interesting to understand how he came to be "the last mathematician that still understood (almost) every subject of mathematics". His dedication to learn new subjects led there.
It was exciting to learn about the way he started out as a student and how he slowly worked his way up to be the greatest mathematician of his time. While reading his book, I sometimes wonder what my future might look like and how I could possibly just imitate a fraction of his greatness.
Towards the second half of the book, I was reminded of how short life actually is. It reminds me that I should sit down, diligently study algebraic geometry and not waste a single second. I feel quite bad for Hilbert to see his friends and comrades die one by one - and then experience the Nazi regime in his last years alive. That was truly not what he and Göttingen deserved.
Nonetheless, his spirit indeed lives on. Almost every day, we mathematics students work with certain tools developed by Hilbert - and may his spirit live on forever.
Hilbert's life is truly fascinating and I find it interesting to understand how he came to be "the last mathematician that still understood (almost) every subject of mathematics". His dedication to learn new subjects led there.
It was exciting to learn about the way he started out as a student and how he slowly worked his way up to be the greatest mathematician of his time. While reading his book, I sometimes wonder what my future might look like and how I could possibly just imitate a fraction of his greatness.
Towards the second half of the book, I was reminded of how short life actually is. It reminds me that I should sit down, diligently study algebraic geometry and not waste a single second. I feel quite bad for Hilbert to see his friends and comrades die one by one - and then experience the Nazi regime in his last years alive. That was truly not what he and Göttingen deserved.
Nonetheless, his spirit indeed lives on. Almost every day, we mathematics students work with certain tools developed by Hilbert - and may his spirit live on forever.
June 15, 2013
"Hilbert had survived [Hermann Minkowski] by more than thirty years. He was still permitted to achieve important work. But who would like to say if his solitary death in the dark Nazi time was not still more tragic than Minkowski's in the fullness of his power?"
Unfortunately that would be how I sum up Reid's biography of Hilbert. It is not a sad work. Hilbert's life was not sad at all. Much of his humour transcends mathematics, and as such Reid's biography is very accessible, and at the same time still manages not to belittle the mathematics.
Still, it is a more tragic, more sad effect to see such a dark end to such a light, optimistic tale of a genius's pursuit of truth. Only to be stopped by surreal politics.
Anyway, a biography to be enjoyed by all types of people, perhaps with the exception of patriots and nationalists, which seem to be often in the way of a mathematician's work (think Hardy).
Unfortunately that would be how I sum up Reid's biography of Hilbert. It is not a sad work. Hilbert's life was not sad at all. Much of his humour transcends mathematics, and as such Reid's biography is very accessible, and at the same time still manages not to belittle the mathematics.
Still, it is a more tragic, more sad effect to see such a dark end to such a light, optimistic tale of a genius's pursuit of truth. Only to be stopped by surreal politics.
Anyway, a biography to be enjoyed by all types of people, perhaps with the exception of patriots and nationalists, which seem to be often in the way of a mathematician's work (think Hardy).
March 26, 2010
Great.
Things get very, very depressing at the end.
Also, this is funny: the author in a preface-type thing says that she wrote the book for laymen. But the publisher, Springer-Verlag, promoted the book only to its existing audience, and that as a result it was only read by mathematicians and scientists. She expressed the hope that mathematicians will continue to read Hilbert, but "that it will also come at last into the hands of the mathematically interested laymen for whom I originally wrote it."
Well, the back cover of this edition says that it "makes this book available to new generations of mathematicians who know the name Hilbert."
Oops.
Things get very, very depressing at the end.
Also, this is funny: the author in a preface-type thing says that she wrote the book for laymen. But the publisher, Springer-Verlag, promoted the book only to its existing audience, and that as a result it was only read by mathematicians and scientists. She expressed the hope that mathematicians will continue to read Hilbert, but "that it will also come at last into the hands of the mathematically interested laymen for whom I originally wrote it."
Well, the back cover of this edition says that it "makes this book available to new generations of mathematicians who know the name Hilbert."
Oops.
August 12, 2023
The best Mathematician biography I've ever read. I'm particularly amazed by how the author, as a non-mathematican, could possibly grasp the spirits of those maths and succintly present the key developements of mathematics at that time so well.
At the moment I put down this book, I had the feeling that I just came back from a time travel to Germany and had lived there for decades, witnessing the rise and fall of the greatest university at that time, the Göttingen university.
At the moment I put down this book, I had the feeling that I just came back from a time travel to Germany and had lived there for decades, witnessing the rise and fall of the greatest university at that time, the Göttingen university.
August 30, 2025
Constance Reid’s Hilbert is an outstanding biography of David Hilbert, widely regarded as the greatest mathematician of his era, second only to his senior, Henri Poincaré. Reid blends historical depth with clear chronological narration, making the story engaging and easy to follow, though the mathematical ideas are still tough to grasp and hard to picture for anyone without a specialist background.
Born in 1862 in East Prussia, David Hilbert pursued a distinguished academic career. After earning his PhD, he moved between various German institutions, as was customary in his field, before establishing himself in Göttingen, where he spent the majority of his professional life. At the time, Europe stood at the heart of scientific and philosophical progress, with countries such as Germany, England and France, and cities like Göttingen, Copenhagen and Cambridge leading the way in academic development.
Early in his career, David Hilbert resolved the Invariant Problem, also known as Gordon’s Problem, and soon after produced a new proof of the transcendence of the numbers e and π. These achievements quickly established his reputation among his peers as a mathematician of great promise. Further breakthroughs followed across diverse areas of mathematics, including his work on the Dirichlet Principle and Euclidean Geometry.
Highly respected within the academic community, David Hilbert was invited to deliver a keynote address at the International Congress of Mathematicians in Paris in 1900. In this historic lecture, he not only gave an inspiring speech but also presented a list of 23 problems that would shape the course of mathematics in the century to come. His aim was to propose challenges that were both difficult and meaningful, capable of driving scientific progress as they were solved. Many of the problems from his famous list, such as the proof of the Riemann Hypothesis, remain unsolved even today, more than a century later, despite tremendous scientific and technological progress.
This period was likely the height of Hilbert’s career. In his personal life, he enjoyed close friendships with brilliant contemporaries such as Hermann Minkowski, but he also endured difficulties in his relationship with his only son, who suffered from mental illness.
Minkowski’s family escaped anti-Semitism in the Russian Empire and settled in Germany during his childhood. A prodigy, he won international recognition at just 18, receiving a Grand Prix in Paris for his solution to the problem of expressing an integer as the sum of five squares. His curiosity extended beyond mathematics into experimental physics: he collaborated with Heinrich Hertz on problems of electricity and later taught a young Albert Einstein in Zurich. Moving freely between mathematics and physics, Minkowski introduced a geometric approach to number theory and played a pivotal role in the early development of relativity, when the theory was still taking shape. His brilliant career was cut short when he died of appendicitis in his mid-forties.
A few years after the death of his close friend, Germany became embroiled in the First World War and was left devastated afterward by inflation and economic hardship. The interwar period saw the rise of Nazism and a decline in Hilbert’s health. During this time, he lost many close friends and collaborators, some of whom fled to the United States, while others were captured or killed. Hilbert himself passed away in the midst of the Second World War.
Born in 1862 in East Prussia, David Hilbert pursued a distinguished academic career. After earning his PhD, he moved between various German institutions, as was customary in his field, before establishing himself in Göttingen, where he spent the majority of his professional life. At the time, Europe stood at the heart of scientific and philosophical progress, with countries such as Germany, England and France, and cities like Göttingen, Copenhagen and Cambridge leading the way in academic development.
Early in his career, David Hilbert resolved the Invariant Problem, also known as Gordon’s Problem, and soon after produced a new proof of the transcendence of the numbers e and π. These achievements quickly established his reputation among his peers as a mathematician of great promise. Further breakthroughs followed across diverse areas of mathematics, including his work on the Dirichlet Principle and Euclidean Geometry.
Highly respected within the academic community, David Hilbert was invited to deliver a keynote address at the International Congress of Mathematicians in Paris in 1900. In this historic lecture, he not only gave an inspiring speech but also presented a list of 23 problems that would shape the course of mathematics in the century to come. His aim was to propose challenges that were both difficult and meaningful, capable of driving scientific progress as they were solved. Many of the problems from his famous list, such as the proof of the Riemann Hypothesis, remain unsolved even today, more than a century later, despite tremendous scientific and technological progress.
This period was likely the height of Hilbert’s career. In his personal life, he enjoyed close friendships with brilliant contemporaries such as Hermann Minkowski, but he also endured difficulties in his relationship with his only son, who suffered from mental illness.
Minkowski’s family escaped anti-Semitism in the Russian Empire and settled in Germany during his childhood. A prodigy, he won international recognition at just 18, receiving a Grand Prix in Paris for his solution to the problem of expressing an integer as the sum of five squares. His curiosity extended beyond mathematics into experimental physics: he collaborated with Heinrich Hertz on problems of electricity and later taught a young Albert Einstein in Zurich. Moving freely between mathematics and physics, Minkowski introduced a geometric approach to number theory and played a pivotal role in the early development of relativity, when the theory was still taking shape. His brilliant career was cut short when he died of appendicitis in his mid-forties.
A few years after the death of his close friend, Germany became embroiled in the First World War and was left devastated afterward by inflation and economic hardship. The interwar period saw the rise of Nazism and a decline in Hilbert’s health. During this time, he lost many close friends and collaborators, some of whom fled to the United States, while others were captured or killed. Hilbert himself passed away in the midst of the Second World War.
February 24, 2025
The writing is a bit dry at times, but the author, who isn't a mathematician (though she's the sister of one), seems to have understood well the scope and importance of Hilbert's work. Obviously, since I don't understand mathematics, I couldn't take advantage of that, but it's a good read for those interested in the subject. Still, the reading was worthwhile even for someone like me, who has never solved a logarithm problem correctly in their life lol
But what surprised me the most was how Reid managed to transport me to Germany from the mid-19th century to the mid-20th century. It was fascinating to see how the country achieved so much scientific progress during such a troubled period marked by wars and other social and political issues. However, the end of the book is depressing because Hilbert passed away near the beginning of World War II and had to spend his last years watching the math department being dismantled by the rise of Nazism and his friends and colleagues being fired and forced to seek refuge in other countries (not to mention those who died of old age, like Klein, or illness, like his best friend Minkowski, who died about 4 decades before Hilbert). It was sad to read about how empty his funeral was because of this.
Anyway, I also liked learning more about other mathematicians connected to Hilbert, like Felix Klein, Minkowski, Weyl, Courant (who was the subject of another biography by the same author)... I loved how Hilbert defended the hiring of the extraordinary Emmy Noether against the sexism of the time (saying something like "this is not a bathhouse"). I particularly enjoyed Hilbert's acid humor, for which he was well known.
The reading was certainly worthwhile and I recommend it to anyone who wants to learn more about mathematicians of the past and perhaps also about German history 🙂
But what surprised me the most was how Reid managed to transport me to Germany from the mid-19th century to the mid-20th century. It was fascinating to see how the country achieved so much scientific progress during such a troubled period marked by wars and other social and political issues. However, the end of the book is depressing because Hilbert passed away near the beginning of World War II and had to spend his last years watching the math department being dismantled by the rise of Nazism and his friends and colleagues being fired and forced to seek refuge in other countries (not to mention those who died of old age, like Klein, or illness, like his best friend Minkowski, who died about 4 decades before Hilbert). It was sad to read about how empty his funeral was because of this.
Anyway, I also liked learning more about other mathematicians connected to Hilbert, like Felix Klein, Minkowski, Weyl, Courant (who was the subject of another biography by the same author)... I loved how Hilbert defended the hiring of the extraordinary Emmy Noether against the sexism of the time (saying something like "this is not a bathhouse"). I particularly enjoyed Hilbert's acid humor, for which he was well known.
The reading was certainly worthwhile and I recommend it to anyone who wants to learn more about mathematicians of the past and perhaps also about German history 🙂
May 20, 2025
David Hilbert (1862-1943) was one of the most important mathematicians in history. He significantly contributed to an incredibly wide range of research fields in mathematics, most notably to the foundations of mathematics and mathematical logic. Perhaps his most spectacular achievement was to formulate, in 1900, a list of 23 mathematical research problems, which inspired and influenced thousands of 20th-century mathematicians.
The author, Constance Reid, a non-mathematician, does a very good job writing about mathematics. The biography also provides a great account of Hilbert’s life, his human side, and his friendships, particularly with Hermann Minkowski. The reader will also learn how David Hilbert had made the mathematics department of the University of Gottingen the world center of the mathematical thought, before Hitler came to power and destroyed everything.
(I have the faintest personal connection to Hilbert: he had been the doctoral advisor of Hugo Steinhaus, who had been the advisor of Jan Oderfeld, who was my advisor.)
The author, Constance Reid, a non-mathematician, does a very good job writing about mathematics. The biography also provides a great account of Hilbert’s life, his human side, and his friendships, particularly with Hermann Minkowski. The reader will also learn how David Hilbert had made the mathematics department of the University of Gottingen the world center of the mathematical thought, before Hitler came to power and destroyed everything.
(I have the faintest personal connection to Hilbert: he had been the doctoral advisor of Hugo Steinhaus, who had been the advisor of Jan Oderfeld, who was my advisor.)
February 6, 2024
A good biography of one of the most important mathematicians of the 20th century. I started it in 2022, put it down and didn’t restart it until early 2024, when I decided to clear out my Goodreads backlog. Good if you enjoy biography and science.
July 18, 2017
An inspirational book for those who wishes to become a mathematician. David Hilbert had a lot of qualities which are role models for mathematicians nowadays.
November 21, 2017
It's not worthy reading, a wasted time.
March 15, 2019
The book is so flat,the writer seems unemotional about The Great Hilbert.But hilbert is the true genius with no doubt.
April 27, 2025
Well written, comprehensive, and informative about the mathematical school of Germany at the end of the 19th and the first half of the 20th century.
December 19, 2025
Honestly had a boring life.
January 3, 2014
I skimmed this. I was looking for the origins of Hilbert's Grand Hotel (which I did not find, but is presumably from a lecture he gave in the 1920s), but it was still an interesting look at the life of one of the great mathematicians of the late 19th & early 20th centuries. Although David Hilbert doesn't appear to have been a very nice person, his foray into skiing, and his obsession with bicycling and gardening were particularly humanizing. Also, it's kind of great to read about someone who talked smack about Einstein.
January 1, 2009
The book is a bit on the dry side for an autobiography. However,
if you like math and/or philisophy it is well worth your time.
Hilbert made some amazing, and deep, contributions to mathematics
and logic. Many of the quotes on the more abstruse topics require
a couple of readings.
if you like math and/or philisophy it is well worth your time.
Hilbert made some amazing, and deep, contributions to mathematics
and logic. Many of the quotes on the more abstruse topics require
a couple of readings.
August 3, 2018
From my Amazon review of January 26, 2016:
Outstanding. Even though the author is not a mathematician, it's clear she took the time to understand Hilbert's mathematical contributions and was able to explain them, in addition to giving great insight into what Hilbert was like as a person.
Outstanding. Even though the author is not a mathematician, it's clear she took the time to understand Hilbert's mathematical contributions and was able to explain them, in addition to giving great insight into what Hilbert was like as a person.
July 19, 2013
Communication and simplification, the two most important elements in math studying, are what I learned from Hilbert.
July 21, 2015
Hilbert -Genius at Work!!!!
June 17, 2015
awesome book! Tells the story story of one of my favourite mathematicians putting it in a historical context.
January 12, 2016
A very good non-technical biography of one of the 19/20th century's greatest mathematicians
May 1, 2017
This is an excellent portrait of the man and the time and place of his life, before and during the war in Germany.
Displaying 1 - 23 of 23 reviews