Between teaching, research, paper–writing, and job applications, last semester was extremely busy for me. Obviously my blogging suffered (my last post was in July!), though I’m glad to see that Greg has been carrying the torch. With less to do this semester, I’m intending to start blogging again regularly. Hopefully my return will inspire Matt to come out of retirement!
Looking back at my old entries, I see that I put an enormous amount of effort into each one, leading to an inevitable decline in their frequency. Now that I’m back, I’d like to get more comfortable with writing posts that are short and friendly—less like Bourbaki and more like Isabel’s blog.
To emphasize my new commitment to casual blogging, I’ve decided to make my first post nothing more than a set of random links. Here goes:
- The Harmonic Series Diverges Again and Again [PDF]: Twenty different proofs that the harmonic series diverges.
- On Proof and Progress in Mathematics (arXiv), by William Thurston.
- Hilbert’s Twenty-Fourth Problem [PDF]: This discusses the “lost” Hilbert problem, which is to formally define notions like homotopy between two proofs of the same theorem, and to decide by what criterion a given proof might be the “simplest possible”.
- The Rise, Fall, and Possible Transfiguration of Triangle Geometry (JSTOR): A fascinating paper about an important subject in 19th-century mathematics which has almost completely ceased to exist.
- Pythagoras’ Theorem for Areas (JSTOR): Let , , and be the areas of the three legs of a right tetrahedron, and let be the area of the hypotenuse. Then .
- You Could Have Invented Spectral Sequences [PDF]: Possibly my favorite title for a math article, ever.
- The Story of the 120-Cell [PDF]: An article about a certain regular four-dimensional polyhedron with 120 dodecahedral faces.