The Importance of Communication Skills in Science
The Poincare conjecture was until recently one of the great unsolved problems in mathematics. Stephen Smale proved the conjecture for 5 or more dimensions in 1961, Michael Freedman proved the conjecture for 4 dimensions in 1982, and Grigori Perelman proved the final case for 3 dimensions in 2003. All 3 mathematicians won Fields Medals for their work (though Perelman declined the award).
Smale's and Freedman's proofs were widely lauded, and both have since landed prestigious appointments: Smale was a professor at Columbia and then Berkeley; Freedman was a professor at UCSD and is now at Microsoft Research. Perelman's proof, in contrast, has generated considerable controversy; he is currently unemployed and lives with his mother in St. Petersburg, Russia.
A fascinating account of Perelman's saga recently appeared in The New Yorker. The gist of the story is that rather than publishing a formal proof of the Conjecture, Perelman posted a series of sketches to arXiv. Other authors subsequently refined the sketches into a full proof. Because these authors did not understand some parts of Perelman's sketch, they inserted some of their own methods in places, and as a result have claimed credit for the final proof. Perelman has renounced mathematics altogether over the dispute.
Authorship is particularly relevant in this case, as the Clay Mathematics Institute has offered a million-dollar prize for a proof. Because Perelman did not publish anything in a peer-reviewed journal, it is not clear that he is eligible.
I think that many researchers believe that if the science is good, everything else will follow. Perelman's case is a cautionary tale: he has clearly done brilliant work, but his mode of presenting his results has cost him dearly.
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on Mon, Aug 06, 06:08PM
From reading Russian language on-line press, I gathered that Perelman does not care about recognition by the world community. He's been a hermit for many years, only formally employed at some math research institute by people who helped him to sustain himself. Yet you made it sound as if he has gone sour on "mathematics" (meaning the science establishment). in my opinion, he is just enough crazy to not care about that. You are right about one thing, though: had he lived in the U.S., he'd be a bum on the streets of S.F. since no U.S. university would have put him on payroll.
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on Mon, Aug 06, 08:08PM
I'm sure the Russian language press has more info, but alas, my Russian is pretty rusty (ya izuchil mnogo l'et nazad i ya zab'il vc'o). From the New Yorker interview, though, it sounds like he is pretty upset with the mathematics community.
I think he could get a job because he is so brilliant - apparently he's had a few offers - but if he were just a little bit less smart, I think you're right that he'd be on the streets. In contrast, if Strang or Freedman were slightly less brilliant, they'd just be professors somewhere a little less prestigious. Being able to interact with other humans makes a huge difference.
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