The big math story in 2006 was the publication of complete proofs of the Poincare conjecture, and subsequent events. In August, Grigori Perelman was awarded the Fields Medal for his role in the proof, which he turned down. At the same time the New Yorker published its famous article about Perelman and Shing-Tung Yau.
Ars Mathematica ran 224 posts for the year. The most popular post (judged by the number of comments) was Michael’s Who are youâ€¦who who, who who, which asked everyone to talk about their favorite subject. The second most popular was my unprovoked attack on category theory, Opinions of Category Theory. The third most popular, interestingly enough, was Hartry Field, which featured a detailed and substantive debate on Field’s interpretation of mathematics.
The post I am personally most proud of is Grete Hermann, which describes the contributions of an undeservedly obscure figure in twentieth century mathematics and physics. My New Year’s resolution for 2007 is to actually complete some of the partially-written posts I started in 2006 (I’m up to 60).