Ars Mathematica

When Gauss called number theory the queen of mathematics, he had in mind its future usefulness to the military-industrial complex. Discuss.

Woah, look at that! The seventh Carnival of Mathematics is up at nOnoscience.

The sixth Carnival of Mathematics is up at Modulo Errors.

If you happen to be an expert on dispersive PDEs, the Dispersive Wiki could use your help.

I neglected to put up a post about the first issue of the Bulletin of the AMS for 2007. Here’s some of the highlights:

• K. Soundararajan describes a recent result of Goldston, Pintz, and Yildirim on gaps between primes. The article provides a taste of what analytic number theory is like.
• Jaikumar Radhakrishnan and Madhu Sudan provide an introduction to Dinur’s proof of the PCP theorem. The PCP theorem, one of the most surprising complexity theory results of the last twenty years. Dinur’s proof is not the original, but provides a new approach to the topic.
• Svetlana Katok and Ilie Ugarcovici explain the relationship between symbolic dynamics and differential geometry. Symbolic dynamics fits perfectly in the computer era, so it always seemed bizarre to me that it was invented purely as a technique in differential geometry.

Now to write up the second issue before the third issue comes out…

Sorry posting has been light. I just moved, which is filled with many non-math-related activities such as unpacking, but also many math-related activities, such as wondering where all of your books went. The chaos is almost to an acceptable level, so posting should pick back up.

Commenter h recommended Borcherd’s lecture notes on QFT. I’ve only just begun reading them, but his Life Cycle of a Theoretical Physicist, which begins the introduction, is incredibly funny.

The May Notices of the AMS features Francesco Mezzadri’s How to Generate Random Matrices from Classical Compact Groups. The mysteriously titled If Euclid Had Been Japanese, by Bill Casselman, discusses an interesting question: what points in the plane are constructible by origami folds rather than ruler and compass? (I’d never heard of this before, but Wikipedia has a page on the subject.)

In this month’s What is…?, Valentin Poénaru answers the question What is an infinite swindle? I’d expected the article to be about the Eilenberg swindle, which is an example of a ring without invariant basis number. Instead, Poénaru describes exotic examples of spaces that are constructed recursively, such as the Whitehead manifold and Casson handles.