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The Honors Class
This eminently readable book focuses on the people of mathematics and draws the reader into their fascinating world. In a monumental address, given to the International Congress of Mathematicians in Paris in 1900, David Hilbert, perhaps the most respected mathematician of his time, developed a blueprint for mathematical research in the new century. Jokingly called a natural introduction to thesis writing with examples, this collection of problems has indeed become a guiding inspiration to many mathematicians, and those who succeeded in solving or advancing their solutions form an Honors Class among research mathematicians of this century. In a remarkable labor of love and with the support of many of the major players in the field, Ben Yandell has written a fascinating account of the achievements of this Honors Class, covering mathematical substance and biographical aspects.
498 pages, Paperback
First published January 1, 2001
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Displaying 1 - 12 of 12 reviews
July 8, 2009
Amazon 2009-01-25, after being freshly reminded of this book's existence by Dick Lipton's mention in CS7530, Randomized Algorithms.
Well, this was certainly packed with information and unhesitating about going into the details -- think of it as a precursor 300 pages to that great tome of essays, The Princeton Companion to Mathematics, just as I like 'em. Unfortunately, the prose was rather frenzied and at times desperately in need of grammatic help, but word choice was strong throughout and there was great material to work with. Yandell managed to find some outstanding new photos, especially of Russian mathematicians, and for that he must be applauded. In no way was the book perfect, though -- I suspect (especially after reading up on him) that Yandell, not unlike Your Humble Reviewer, dips into the weed-and-speed tills with some frequency, and that just doesn't make for a stable book. Perhaps if he'd restricted himself to jaunty 150-words-or-so reviews of the papers mentioned, he'd have done better =D.
Actually, I just bumped it up to four stars from three because of the absolutely awesome bibliography. Hats off, Yandell! Let's see another effort before your heart explodes.
Well, this was certainly packed with information and unhesitating about going into the details -- think of it as a precursor 300 pages to that great tome of essays, The Princeton Companion to Mathematics, just as I like 'em. Unfortunately, the prose was rather frenzied and at times desperately in need of grammatic help, but word choice was strong throughout and there was great material to work with. Yandell managed to find some outstanding new photos, especially of Russian mathematicians, and for that he must be applauded. In no way was the book perfect, though -- I suspect (especially after reading up on him) that Yandell, not unlike Your Humble Reviewer, dips into the weed-and-speed tills with some frequency, and that just doesn't make for a stable book. Perhaps if he'd restricted himself to jaunty 150-words-or-so reviews of the papers mentioned, he'd have done better =D.
Actually, I just bumped it up to four stars from three because of the absolutely awesome bibliography. Hats off, Yandell! Let's see another effort before your heart explodes.
August 20, 2018
A fine summary. There are a lot of gaps in the math - I had to supplement my reading with Wikipedia and Wolfram - but overall this was a good jumping off point.
March 10, 2024
The book provides a good historical account of Hilbert's problems and the efforts of mathematicians to solve them. As the title suggest, it is more interested in the solvers than in the solutions. The core of the book are the vivid biographies of several important mathematicians, their way of thinking, and their character. The author has done a thorough job in this regard, using many different sources and (when possible) consulting with the protagonists or people who knew them.
Each chapter is basically a treatment of one of Hilbert's problems and the main mathematicians involved in the efforts to find a solution. The book usually provides a description of the problem, its relevance, and its difficulty, but except for some of the most accessible problems, the technical content is probably hard to follow for people without mathematical background. In the end, the book is more interested in the people than the problems.
The main accomplishment of the book lies, I think, in showing the lives of mathematicians in a vivid way, and highlighting the particular role that open problems play in their lives and profession. Highlights for me are the chapters devoted to the third (for its biography of Max Dehn) and tenth problems (for its general interest and the way it showcases the collaborative aspect of mathematics).
Each chapter is basically a treatment of one of Hilbert's problems and the main mathematicians involved in the efforts to find a solution. The book usually provides a description of the problem, its relevance, and its difficulty, but except for some of the most accessible problems, the technical content is probably hard to follow for people without mathematical background. In the end, the book is more interested in the people than the problems.
The main accomplishment of the book lies, I think, in showing the lives of mathematicians in a vivid way, and highlighting the particular role that open problems play in their lives and profession. Highlights for me are the chapters devoted to the third (for its biography of Max Dehn) and tenth problems (for its general interest and the way it showcases the collaborative aspect of mathematics).
January 8, 2018
A meandering, expose- more historical than mathematical, about Hilbert’s Problems. I have a lot of math background, but have been out of the game for a few years, and at times reading this brought me back to the joy of mathematics. (I miss ideals and Kolmogorov) But with a text like this, it’s really difficult to bridge the complicated math in a casual enough way that most will understand. (I’m not terribly sure what kind of audience this book is targeted for. Maybe someone seriously studying something related would be interested in the history, but of course for the math itself they’d turn elsewhere. On that note, there were times where I thought there were too many analogies to try and get the point across.)
Yandell took ten years to write this, and me more than half a year to read. There were definitely times where I was a bit tired from his jumping from one mathematician to another had, but there are certainly nuggets in here that are interesting. Doesn’t quite do the job of making me drop everything and return to my PhD life, but a valiant effort.
Yandell took ten years to write this, and me more than half a year to read. There were definitely times where I was a bit tired from his jumping from one mathematician to another had, but there are certainly nuggets in here that are interesting. Doesn’t quite do the job of making me drop everything and return to my PhD life, but a valiant effort.
November 6, 2024
One of the better pop maths books ever.
Yandell is literal and fussy and his biographies are just lists of disconnected facts. But he is a master of the material and put in vast amounts of work to dig up facts you struggle to find elsewhere (in English). It is hard to do better than this without formalism (and it's of course still vague and suggestive).
He doesn't actually say who solved the first problem...
He completely blanks the question of Kolmogorov's sexuality, except accidentally by emphasis: Alexandrov gets about 6 pages while Anna Dmitrievna (his wife) is only mentioned once.
Yandell is literal and fussy and his biographies are just lists of disconnected facts. But he is a master of the material and put in vast amounts of work to dig up facts you struggle to find elsewhere (in English). It is hard to do better than this without formalism (and it's of course still vague and suggestive).
He doesn't actually say who solved the first problem...
He completely blanks the question of Kolmogorov's sexuality, except accidentally by emphasis: Alexandrov gets about 6 pages while Anna Dmitrievna (his wife) is only mentioned once.
February 19, 2022
The level of research of this book is mind-blowing and frightening. (It has about a hundred pages of notes and bibliography.) And how can someone know so much mathematics? There didn't seem to be a Hilbert problem that Yandell didn't have a competent background on. Or is that normal for first-rate mathematicians?
October 14, 2018
The obvious problem is that the stories are similar.
July 14, 2008
In the early 1900's mathematician David Hilbert listed a number of mathematical problems that he believed should be addressed and solved in the near future. This book describes those problems and the efforts (successful or not) toward solution.
Overall a good treatment and well written. But there are some issues.
The author mixes biographical information (sometimes quite detailed) with the mathematics, making it somewhat confusing. Along a similar line, he doesn't recast Hilbert's original statement for the non-mathematician. Nomenclature is also sometimes a problem. He refers to "analytic" functions, but doesn't make clear what it means (I think it means satifying the Cauchy-Riemann conditions, but that's a guess).
One of Hilbert's problems was making physics axiomatic. Needless to say, not much progress has been made along this line.
Recommended with reservations.
Overall a good treatment and well written. But there are some issues.
The author mixes biographical information (sometimes quite detailed) with the mathematics, making it somewhat confusing. Along a similar line, he doesn't recast Hilbert's original statement for the non-mathematician. Nomenclature is also sometimes a problem. He refers to "analytic" functions, but doesn't make clear what it means (I think it means satifying the Cauchy-Riemann conditions, but that's a guess).
One of Hilbert's problems was making physics axiomatic. Needless to say, not much progress has been made along this line.
Recommended with reservations.
February 17, 2014
A nice compendium of Hilbert's problems delivered at the International Congress of Mathematicians in Paris in 1900 and it's solvers. It mingles the biography of the solvers with a high level description of the problem and the solution. I have abandoned it more than once but this time resolved to finish reading it (I skipped the appendix which is the actual transcript of Hilbert's
description of the problems). Couldn't gain much understanding on the Math (except in some lucid passages) but the biographies showed a really humane side of these great mathematicians without being too detailed and boring.
This book can be a good beach side read for those interested in Math and Mathematicians :).
description of the problems). Couldn't gain much understanding on the Math (except in some lucid passages) but the biographies showed a really humane side of these great mathematicians without being too detailed and boring.
This book can be a good beach side read for those interested in Math and Mathematicians :).
October 22, 2013
A medium to advanced book requiring "hands-on experience" with enough mathematice to know what is being discussed in the book. Yandell does a wonderful job summarizing otherwise hard to access material. I would recommend having Wikipedia handy, and maybe some of your old math or maths(UK) books handy. I'm an avid maths experiementer and love dabbling in things I know little about. However, once I get into a difficult subject, I have no problem becoming enough of an expert to help other people understand it. This book is a great teaser to get you into Grad School if need be.
August 22, 2010
I had to re-purchase this book cos David Altman stole my copy! Really fascinating stuff... this is probably my favorite pop-math book of all time. The problem with most books of this sort is that they're either too superficial or too detailed. This one gets it just right.
July 3, 2008
Yes, I'm a math geek, but this book is actually a very good historical account of the last century in mathematics.
Displaying 1 - 12 of 12 reviews