Via Neighborhood of Infinity, I came across the Flyspeck Project, a project to provide a computer-checked proof of the Kepler conjecture.

The project who proposed by Thomas Hales, who has the only published proof of the theorem. His proof already includes some computer calculations, and turned out to be too complicated to be fully checked by peer review. A complete computer-checked proof would remove any doubts.

The Wikipedia entry links to this elementary introduction by Hales to the proof, Cannonballs and Honeycomb.

I spotted an interesting paper on arXiv with a totally self-explanatory title: On the uniformization of algebraic curves.

All analysts are uptight nerds and all algebraists are dirty hippies. Discuss.

A couple of years ago, the Notices of the AMS featured an article on noncommutative geometry a la Connes: Quantum Spaces and Their Noncommutative Topology by Joachim Cuntz. The hallmark of this approach is the heavy reliance on K theory. The first few pages of the article are fairly elementary (and full of intriguing pictures), before the K theory takes over.

I’ve come across an interesting weblog devoted to the philosophy of mathematics: Philosophy of Real Mathematics, by David Corfield.

H. Jerome Keisler has made freely available his calculus textbook, Elementary Calculus: An Approach Using Infinitesimals. The book is based on Abraham Robinson’s rigorous foundations for infinitesimals.