Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles

A very interesting history of the field of topology from its beginnings in Poincare's time through the present, when one of its most elusive mysteries was finally proven for all dimensions. There are no equations in the book, but one does have to be able to visualize some complex topography to follow some of the more challenging arguments.

While I found the history, the math, and the characters fascinating, I finished the book feeling that the forest was lost for the trees. A lot of time was spent on the stepping stones, blind alleys, and breakthroughs on the way to the proof, little time was spent describing the implications of the conjecture. In the jacket notes, and a little in the introduction, it is promised that if proven true, show more then the conjecture it would make it possible to know the shape of our universe.

I would have given the book an extra star if, after wading through the patient and careful explanation of topography and the conjecture, there was one more chapter that had taken that knowledge, stepped back, and shown the implications of the Poincare Theorem in the context of the geometry of the universe and how the tools developed in the proof could be used to determine if the universe is flat, spherical, hyperbolic, or other.

Other than that quibble, a very enjoyable and engaging book. show less

Necessarily shallow, but the author tries harder than most popular math articles, which I appreciated. The dozens of capsule biographies (born in xxxx, son of xxxx, went to high school at xxxx, etc.) were extremely tedious and almost useless for learning anything about the people involved. With that said, it was a very fast read, and enjoyable enough.

Interesting history of an abstruse mathematical conjecture. I would have preferred more mathematical explanation, but that would make it less accessible.

The writing is mediocre, and in particular, the author should work on trying to be cute less often. There were too many attempts at neat turns of phrase or jokes that completely fell flat. Write well, but don't call attention to yourself.

More importantly, though, the mathematical descriptions were lacking! I know it's a hard subject, but if I couldn't follow what was going on mathematically, I don't know how people without a math major under their belts could. If this were more of a human drama story, then the mediocre math would be fine, but the human drama doesn't really get started until the last fifty pages or so, with petty squabbles over priority and disses in print and journal publication procedures.

The author seems to try to get show more human drama flowing in the early pages, as every single mathematician mentioned gets a few paragraphs of biographical information, but dozens of snippets of encyclopedia-type information do not add up to an interesting story.

Finally, does the author have a point? I couldn't find one. I guess the argument is that it's just a biography of a math problem, but good biographies have, if not necessarily something as full-blown as a thesis, at least a point. And I fail to see the point of this book. show less

Bon livre de vulgarisation . Malheureusement mes pauvres connaissances en algèbres et en géométrie ne m'ont pas permis de suivre l’évolution des démonstrations au fil du livre.
A relire dés que possible !

Une histoire des mathématiciens qui se sont frottés à la conjecture de Poincaré tout au long du XXème siècle. Riche en portraits.
On n'apprend pas grand chose sur la théorie en elle même, l'effort d'utilisation de concepts compréhensibles par le grand public pour tenter d'expliquer les idées de la topologie les rend paradoxalement confuses et peu "manipulables".

Avreste mai pensato che il percorso storico e teorico che ha portato alla soluzione di questa celebre congettura, potrebbe assumere i contorni di un romanzo giallo? In questo libro alla storia matematica si intreccia, infatti, anche l'enigma della figura di Perelman, il matematico russo che riuscì a dimostrare la congettura, ma che ancora rifiuta qualunque riconoscimento.