The Importance of Communication Skills in Science

Posted by Geoff Davis at 12PM on 07/27/07 | Categories: Skills | 2 comments

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.