Ars Mathematica

I’ve gotten complaints recently about Ars Math’s comment registration system, so as an experiment, I’ve enabled users to post comments without registering. Here’s hoping that I get to spent part of the next 24 hours not deleting spam…

Mark Srednicki has written a new textbook on quantum field theory. The final version is not available electronically, but a prepublication draft is.

It’s common for authors to take down the manuscript when the book is published, so it’s nice to see it when an author bucks the trend. Srednicki adopts a reasonable compromise in keeping the final-but-one version available on his site (he warns “This draft contains numerous errors (mostly minor) that are corrected in the published version”).

Finally, somebody (Rudbeckia Hirta) willing to tell the truth about the harmonic series:

I know, you’re looking at this series and you don’t see what I’m warning you about. You look and it and you think, ‘I trust this series. I would take candy from this series. I would get in a car with this series.’ But I’m going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.

Via Let’s Play Math.

Sean at Cosmic Variance notes that NASA has discovered that everyone is apathetic about their new planned mission to the Moon and then Mars, and that they are in the market for a celebrity spokesperson to change that. They are throwing around obvious names, like David Duchovny and Patrick Stewart, when the answer is obvious. There is only one man for the job of selling the new Mars mission:

Dave Chappelle (warning: long, not safe for work, and you probably won’t think it’s funny).And if NASA is looking for a marketing slogan, they could do worse than what John Baez says here: “the scientific equivalent of putting a goldfish bowl on top of Mount Everest.” Think about it — we’ll never know what’ll happen to that goldfish unless we try. Dare to dream.

When I was writing the year in review post, I did a quick websearch to refresh my memory on the Perelman-Yau story. (Reading about it I found the idea that the big story of 2006 was a public personality conflict between prominent mathematicians was too depressing to contemplate, so I ended up skipping the details.)

Wikipedia has two incredibly detailed articles about the subject. One provides a summary of Manifold Destiny, even going so far as to list every interviewee. The other describes the war of words between Yau and Gang Tian waged in Chinese newspapers and on the web. The story is not all that interesting, but references to it appear from time to time.

One twist in the story reported by Wikipedia that’s new to me is that Sujit Nair discovered a section in the Cao-Zhu proof of the Geometrization Conjecture that duplicated some results in Kleiner and Lott’s manuscript. Cao and Zhu issued an erratum acknowledging the duplication.

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 you…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).