In my mail: The Best Writing On Mathematics 2011 (Mircea Pitici, ed.) from Princeton University Press. Just to get this out of the way: I’m in here! They reprinted my compressed sensing article from Wired.
You might now be wondering: are there really enough popular math articles published in a given calendar year to fill up an anthology? No. There are not. But this is part of the charm of what Pitici has done. His very broad definition of “writing on mathematics” allows him to include useful professional advice for young mathematicians from Andrew Schultz, reflections on a career in math education from John Mason, and academic-yet-readable philosophy (“What Makes Math Math?”) from Ian Hacking, whose The Emergence of Probability is my favorite book in history of mathematics.
I especially like Mel Nathanson’s pessimistic take on massive collaboration in mathematics — because it is a forcefully written, carefully argued case for a position with which I mostly disagree. “I would guess that even in the already interactive twentieth century,” he writes, “most of the new ideas in mathematics originated in papers written by a single author.” I would guess otherwise — at least if you restrict to the second half of the century, when joint papers started to become really common. Mel calls me out for writing about Tim Gowers’ Polymath Project in the New York Times with “journalistic hyperbole” — and here he is right! It is very hard, in the genre of 300-word this-year-in-science snippet, to keep the “gee whiz!” knob turned down and the “jury is still out” knob turned up.
Gowers claims the classification of finite simple groups as a pre-Internet example of massively collaborative mathematics. Nathanson agrees, but characterizes the classification as fundamentally uninteresting, “more engineering than art.” What would he say, I wonder, about recent progress towards modularity of Galois representations? It’s very hard to imagine him, or anyone, seeing everything that’s happened in the last 15 years as a mere footnote to Wiles. (But maybe some of the experts who read this blog would like to weigh in.)
Recalling Mark Kac’s famous division of mathematical geniuses into two classes, ordinary geniuses and magicians, one can imagine that massive collaboration will produce ordinary work and, possibly, in the future, even work of ordinary genius, but not magic. Work of ordinary genius is not a minor accomplishment, but magic is better.
Yes, but: magic can only happen in the already-enchanted environment created by the hard work of many minds, alone and in teams. Math is like earthball.