The Hilbert Challenge: A Perspective on Twentieth Century Mathematics Hardcover – 23 Nov 2000
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For those who are interested in the genesis and influence of the Hilbert Problems, I strongly recommend .... the recent book by Jeremy Gray (Felix Browder, retiring President of the American Mathematical Society)
About the Author
Jeremy Gray is Senior Lecturer in Mathematics at the Open University. His research interests lie in the history of the mathematics of the 19th and 20th centuries, and in the philosophy and social significance of mathematics. He is the author or editor of nine books, most recently The Symbolic Universe: Geometry and Physics 1890-1930 (OUP 1999).
Top customer reviews
Hilbert's list of the outstanding problems in mathematics, without a doubt, shaped both the mathematics and physics of the past century or so. The list of those who attempted to solve Hilbert's problems, or who became involved on its periphery reads like a who's who of both sciences.
The book itself cannot be described as for the lay reader, it presumes a knowledge of mathematics that is broad and beyond most without some formal training, though not necessarily to degree level. The book glosses over many points and casts throwaway lines about proofs which are central to its theme. Do we perhaps discern the hand of an over-enthusiastic editor, keen to keep the book within certain limits, or for a certain market? The book had the potential to be an important text on the history of its subject and missed the opportunity.
That being said it is very readable and sheds light on interesting areas. Its technique of deferring summary notes not to footnotes, but to highlighted boxes on the page works well and contributes to its overall accessibility.
At the end of the day the reader can't help feeling that the opportunity was missed, but only narrowly so. On finishing it you are left with the feeling that you are not quite satisfied and yet it is difficult to say exactly why...
Fair enough, if you skip the symbols and numbers, the narrative hangs together well, but without understanding the nuances of exactly what Hilbert was asking for with his problems (the Challenge consisted of a number of problems) I don't believe readers can get the best out of this book. Shame.
Like "A Brief History of Time", the story is excellent and compelling, but it needs someone - and I'm not voluteering at this stage - to write a layman's version of the Hilbert story.
A missed opportunity for one of the best popular mathematics books of the year? Maybe. I do, though, remain piqued that the cover notes suckered me in to buying this book - some sort of synaptic health warning should be there!
Most helpful customer reviews on Amazon.com
It is easy to read and well explained, even if you don't grasp the full maths, still there is a story around every of the 23 problems that lets you understand the implication, and the full drama of its solution.
It is a nice biography of Hilbert 'the man', intertwined with the 23 problems, so it does not get boring like some biographies do with endless lists of calendar-facts.
There is even a full translation of the original speech he gave in Paris in 1900, which otherwise would be impossible to find.
The problems itself are well explained, as well in the timeframe of 1900, when first posed, as later in our time when maths was ready to solve them. The author did a good job also telling which of the problems really were important, really gave mahts further problems to think about, and which problems didnt give rise to new mathematical areas, and therefore became more or less curiosities after solution.
Reading this book gave me a feeling of how beautiful maths can be, how unexpectedly some problems can and cannot be solved, and evokes some of the drama of the worlds biggest minds at work.
If you are interested in maths and/oir in science and great minds: this is an excellent read!
The book has three main problems that make it unenjoyable and quite tedious to get through.
The first problem is that the mathematical problems are not sufficiently well explained. In some cases, the problem and it's math are not explained in sufficient depth. In other cases, the problem is not clearly explained and comprehensible. In yet other cases, the problem's application or usefulness is not explained well. Finally, some math is explained so cursorily that it might as well not even have been discussed.
The second problem is that the layout of the book made very little logical sense. First, the author split the problems into various groups. Then, the author split the timeline into various sections: Pre-1900, 1900-1918, 1918-1945 and 1945-1999. He then proceeded to discuss some of the problems in each of the timelines. At each step, you've lost the entire train of thought from the previous section, and it becomes hard to understand what, if any, logical flow or consistency there was in the development of the work on Hilbert's problems or anything that lead from it.
The third and most serious issue against the book is that the author briefly introduces the "23" Hilbert problems and then subsequently expects the reader to understand what "Problem 10" is every time he refers to it, and exactly how it relates to all the other problems. There are quite a few sentences which refer to several problems by number and unless the reader is constantly referring back to the brief summary of all the problems, the sentence might as well have been in martian. After a few dozen pages of playing this "refer to the problem list" game, I became so frustrated that I just gave up and read the book.
Some minor problems include the fact that only 223 pages of the book are by the author; the rest is a translation of Hilbert's 1900 talk. (That is, less than 75% of the book is what the book is supposed to be about.) Another problem for me is that the paper is high gloss. It looks very nice at a glance, but when you try to read it, you are often faced with glare unless you orient the book perfectly with respect to the light source(s) - a problem I ordinarily face only with magazines.
Another minor problem, which may be interpreted as a positive thing by many (and I welcome that interpretation), is that the author spends a fair bit of time discussing social, governmental political and educational political aspects of countries, universities, and mathematicians. Except in a few minor cases, these things seem highly tangential to the work at hand, and although somewhat entertaining, distract from the intent of the book.
All in all, I found myself about half way through finishing it just so I could put it down and start another book, and preferably one completely unrelated to the topic. The author made such a hash of the subject that, despite finding several other interesting books on Hilbert and his problems here on Amazon, I have no interest whatsoever in reading them and actually finding out about things.
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