Poincare conjecture

A comprehensive article at The New Yorker on Perelman, Poincaré conjecture and the politics of math. Perelman, as you might have read, refused the Fields medal - the nobel prize like award for math. From the article,

Mikhail Gromov, the Russian geometer, said that he understood Perelman's logic: "To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness." Others might view Perelman's refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. "The ideal scientist does science and cares about nothing else," he said. "He wants to live this ideal. Now, I don't think he really lives on this ideal plane. But he wants to."

More like this

The August 28 issue of The New Yorker features this magisterial article about the Poincare conjecture. The focus of the article is on the priority dispute between Grigory Perelman on the one hand, and a team of Chinese mathematicians led by Harvard's Shing-Tung Yau on the other. According to the…
To continue this conversation about the state of science, here is an article that discusses the breakthroughs of 2006, starting with an award given to a mathematician for solving a 100-year-old mathematical mystery; The work of a reclusive Russian mathematician who solved a 100-year-old mystery…
There's an interesting article in the Times today about Grisha Perelman and the Poincare conjecture: Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the…
Perelman quit the world of mathematics in disgust four years ago. His decision to spurn the Fields Medal may have been driven by a sense that his fellow mathematicians were not worthy to award it. -Reported in Guardian "his fellow mathematicians were not worthy to award it" Ah. If so, you go,…

Gromov's comments seem to be appropriate. An unfortunate aspect of current mathematics, as pointed out in http://www.newscientist.com/chan.../ mg19125661.400 is
"The underlying issue that emerges when you add together Perelman's work and attitude, the Chinese claims, and the problems of attributing proper credit, is that mathematicians are finding it increasingly difficult to decide whether or not something has been proved."
As it is papers are getting increasingly long and difficult and is often difficult to find referees. Announcement, postings of manuscripts at different sites, constant changes in these seem to have added to the problem. About another well-known problem for which solutions were announced in 98 and a paper claiming the solution appeared this June, I received the follwing comments from another who worked on the same problems:

"That paper has a rather long history, as you
 probably know. Anyhow, I should just indicate that it has
 40 previous versions (I have copies of most of them), in which
 one can literally observe plagiarism, including copied notions, notation
 (at times), and even local mistakes.
 ...
 However, it seems that the editor decided to ignore all that and publish
 the paper without any prior notification.
 I'm not sure what can I do now, and whether it is worth doing. I can
 only quote Grisha Perelman, who said in a somewhat related matter, that
 mathematicians are usually quite honest, but they
 are (somehow) willing to tolerate such a phenomena."