Poincaré’s Prize

I recently finished reading the book Poincare’s Prize, by George Szpiro. The book covers the history of topology and of Henri Poincaré, the attempts to prove his famous conjecture, and the techniques that were developed along the way. Proving the conjecture was one of the seven Millennium Prize problems that were published by the Clay Mathematics Institute, along with million-dollar bounties for each. A proof of the conjecture was finally completed in papers published by the enigmatic Grigori Perelman in 2002 and 2003. This achievement, though, was surrounded by several strange occurrences:

• Perelman refused to accept a Fields Medal for his work, becoming the first person to ever refuse the honor. In an article in the New Yorker, he suggests that his refusal was motivated by a perceived lack of ethical standards in the mathematics community.
• Perelman also refused to submit his work in accordance with the Millennium Prize judging criteria. As of now, the prize remains unclaimed.
• A pair of Chinese mathematicians released a controversial paper around the time that other mathematicians published papers on Perelman’s work (which were intended to clarify his work and present a full proof of the Poincaré conjecture). The Cao-Zhu paper initially contained language claiming that it was, essentially, the first proof of the Poincaré conjecture. This is a position that has not been accepted by the mathematics community at large. Additionally, a section of the Cao-Zhu paper was determined to be plagiarized from the work of the other aforementioned mathematicians.

Even though I haven’t ever really been seriously interested in topology (nor displayed much aptitude for the frequently mind-bending concepts involved), I thoroughly enjoyed the book. In reading it, I began to feel that perhaps math educators (at all levels) were wrong in focusing their attempts to interest students in math solely on applied examples. I honestly can’t remember any math teacher or professor with whom I’ve interacted making much of an effort to interest students in pure math. Granted, careers in pure math are few and far between, but it seems wrong to practically steer students away from the field.

Through the book I also learned of the existence of arxiv.org, an e-print archive maintained by Cornell. I guess my prior searches for academic papers always wound up leading me to individual school sites, and not this archive. (They also appear to have a somewhat hostile attitude towards indexers!) I may have to spend some quality time plowing through the computer science sections to find articles to read — I’m sure I could find lots of things to interest me in there.

Apart from that, having been bitten by the math history bug, I now have The Artist and the Mathematician sitting on my book queue. I had read the short book Chance, by the same author, recently as well, and thought enough of it that I figured I’d give this other book a shot too.