But I was also skeptical. Why? First, most attempts at proving such an important problem turn out to be flawed, even if they initially seem credible. Second, I've noticed that in recent years, virtually all successful efforts at solving key mathematical puzzles have come from people whose exceptional brilliance was already recognized via standard channels.
Consider perhaps the most impressive mathematical feat of our era, Grigori Perelman's proof of the Poincare Conjecture. A great deal of media attention focused on Perelman's apparent eccentricity: he lived with his mother, declined the Fields Medal, and now even seems to be declining the million-dollar Millennium Prize. But while he fits the "lone genius" cliche, he was hardly an unrecognized lone genius. As a high school student, he received a perfect score at the International Mathematical Olympiad, an incredibly difficult feat accessible to only an elite few. He went on to receive a Ph.D. from what is now St. Petersburg State University—one of the top institutions in Russia—and held positions at elite American math departments like SUNY Stony Brook, NYU's Courant Institute and UC Berkeley. Apparently he was offered professorships at Stanford and Princeton after leaving UC Berkeley, but turned them down in favor of returning to the Steklov Institute in Russia.
In other words, Perelman made his way to the very top of the mathematics profession long before he vanquished the Poincare conjecture.
Or consider Andrew Wiles, whose proof of Fermat's Last Theorem in the 1990s was easily the most widely recognized mathematical accomplishment of the decade. When he proved the theorem, he was a professor at Princeton University, which is as good a gig in mathematics as one can imagine. He was an undergraduate at Oxford, obtained his Ph.D. at Cambridge, and held a professorship at Oxford in between stints at Princeton.
Compare these examples to some of the widely publicized false proofs from recent years. In 2006 we saw a flawed attempt at solving the Navier-Stokes Equations (another of the Clay Mathematics Institute's "millenium problems") from Penelope Smith of Lehigh University. Smith was hardly a crank (which is why her attempt received so much attention) but her professional background didn't come close to Wiles or Perelman. She was an associate professor, never promoted to full professor despite almost three decades since her Ph.D., at a department in the lower half of the National Research Council rankings.
I don't mean to be elitist—I could never be a math professor anywhere. And my evidence is admittedly anecdotal. But I do see a compelling pattern here: more than ever before, the most compelling advances in mathematics come from people who were already at the top of their profession. The era of Swiss patent clerks making major contributions is over.
Is this because our current set of institutions is better at identifying talent early on? Because math at the research frontier has become so ungodly complicated that one needs to be plugged into the research elite to understand it? Or, on a related note, because ever more arcane mathematics requires more time to understand deeply, driving up the traditionally low median age of mathematical accomplishment and offering more time for our institutions to recognize geniuses before they make their greatest advances? All of the above?
I can't say.