This is really very cool. In several ways.
First: For the past year or so, there has been a remarkable website called Math Overflow where research mathematicians gather to swap ideas, to ask for help when they get stuck, and to offer help when they can. Frequent contributors include the Fields Medalists (a Fields Medal is roughly the mathematical equivalent of a Nobel Prize) Terry Tao, Tim Gowers, Bill Thurston and Richard Borcherds. Others who have popped up from time to time include Vaughan Jones (yet another Fields Medalist), John Tate, whose thesis reshaped modern number theory, and Peter Shor, the pioneering figure in quantum computation. And every day, one runs across dozens of other folks who nearly any top math department would be proud to have (and in many cases are proud to have) on their faculties. If you already know a lot of math, you can get a hell of an advanced education browsing this site.
Second: For the past nine years or so, the Norwegian government has presented an annual Abel Prize for lifetime mathematical accomplishment. The winnners have been well chosen without exception — several are past Fields Medalists. The Abel prize differs from the Fields Medal in that you get it when you’re old (the Fields Medal must be won before age 40) and that it comes with about a million bucks (similar to the Nobel Prize). The Fields Medal has a longer and therefore more glorious history, but it’s clear that the Abel Prize is becoming similarly prestigious.
Third: This year’s Abel Prize was awarded to John Milnor for his dazzling career in topology. As part of the ceremony, Tim Gowers, the Fields Medalist and frequent Math Overflow participant, was called on to give an exposition of Milnor’s work, which you can watch here or read here. Gowers’s talk was to be given immediately following the announcement that Milnor had won, and therefore had to be prepared in great secrecy. (Milnor himself was not notified until one hour before the public announcement.)
Fourth: Grasping the essence of great work is not always easy, even for a Fields Medalist, especially when the work is as dramatic as Milnor’s. (And especially when, as in this case, the expositor and the prizewinner work in very different areas of mathematics.) Nobody I know of would want to write an exposition of someone else’s pathbreaking work without consulting a few colleagues to make sure they hadn’t missed the point. Gowers, working in top secrecy, didn’t have this luxury. But he did have Math Overflow.
So fifth: Gowers decided to post some questions to Math Overflow intended to check and expand his understanding of what Milnor accomplished and how. But he had to be very very careful that nobody figured out what he was up to. So instead of asking directly about Milnor’s work, he cleverly formulated his questions in a way that disguised the direct connection to Milnor — feigning, for example, a particular interest in four-dimensional topology, whereas Milnor’s most spectacular discoveries concern phenomena in seven dimensions and higher. The questions Gowers posed were just enough related to Milnor’s work to elicit some insight — but just enough unrelated to throw people off the scent. It worked! Read Gowers’s blog for the full story.