There’s a prize of one million dollars for solving the Poincaré Conjecture. The yellow brick road to that payoff leads past many of the usual and important milestones in academia: conferences, papers, peer-reviewed journals. As a recent article in The New Yorker makes clear, it’s also important to circulate early versions of a proof strategically, to be sure the flaws are caught before you stake your claim to a discovery.
Russian mathematician Grigory Perelman went through many of the usual processes, according to the article. There was a Berkeley fellowship, contact with many distinguished mathematicians, job invitations from all over, and the like (if there is a “like” when one gets to those heights). But at age twenty-nine, Perelman chose to move back to Russia, to a low-paying university post and physical isolation from the very thinkers he had sought out.
Home. Alone. But not quite alone. Here’s the sentence that even in 2006 retains its power to astonish–and I hope it retains that power for a long time, though the article makes relatively little of it.
The Internet made it possible for Perelman to work alone while continuing to tap a common pool of knowledge.
Individuality and community, enacted at one of the higher reaches of human intellectual accomplishment. But it gets better:
On November 11th, Perelman had posted a thirty-nine-page paper entitled “The Entropy Formula for the Ricci Flow and Its Geometric Applications,” on arXiv.org, a Web site used by mathematicians to post preprints–articles awaiting publication in refereed journals. He then e-mailed an abstract of his paper to a dozen mathematicians in the United States … none of whom had heard from him for years.
Within seven months, Perelman completed the trilogy of Internet postings that seem to have proved the Poincaré Conjecture.
Questions of temperament aside, Perelman’s choices illustrate some of the enormous potential consequences of the Information Age and its media. Scholarship and the communities that form around it will be slow to change, and that’s not all bad. Education is conservative as well as liberal in senses that have nothing to do with partisan politics. Yet I look at the Perelman story and I’m struck by two things. One is that we are at the very outset of these changes, and many of us alive today will live to see dramatic and far-reaching shifts in higher education involving not only learning but also the community of scholars. That’s pretty obvious. The second striking thing, however, is that the New Yorker piece spends almost no time considering this revolution. I speculate that that’s either because that fundamental paradigm shift hasn’t registered on the authors … or because they’re already taking it for granted.
I’ll close with a small troubling thought. It is entirely possible for us in the scholarly community and in higher education generally to take something for granted before it’s actually registered on us. If that happens, we will be blown before the wind instead of steering by it.
How should we keep that from happening?
I would argue that at it’s best education is conservative and liberal in the best senses of those words — embracing ideals of conservatism and liberalism that we should all seek to understand and apply equally in appropriate situations. It’s a shame we have such a hard time understanding how these two ideals can coexist and even compliment each other.
Did you see the article on the Perelman and the Poincaré Conjecture in the New Yorker a few weeks ago?
Agreed. 🙂
And yes, it’s the article that triggered the post. I had read about Perelman and the conjecture earlier and meant to blog about it at the time. Cleaning house (old house, apparently a bottomless pit of stuff) last weekend I ran across the old NYer (see, that’s why I saved it, augh) and read the story.
I think “shame” is a very good word in this context, by the way. A national shame.
It was a good article. I think the authors consider Perelman to be unique, or at least very rare. Math is a joy, a profession, but not necessarily work for him. He seems to be happy to share his work, but he prefers to let it speak for itself rather than go through the administrative hoops set up by the Academy.
What’s nice is that the Academy appears to be accepting of great work even if the scholar won’t participate. I wonder how quickly things will change because of his approach. Is he accepted because of the magnitude of his work, despite his detachment? Would he be as accepted if he hadn’t solved such a monumental problem?
I agree that the internet has the potential to transform scholarship, but I think we’ll have to see more anomalies like Perleman before things begin to change.
On a lighter connection, the Poincare Conjecture and another important math problem will be the subjects of a talk at University of Mary Washington on Wed. Nov. 8 at 7:30, room 100 of Jepson Hall.