I’d wish everyone a happy new year, but clearly the mathematically inclined all refuse to recognize arbitrary time divisions.

I’ve been tipped, via e-mail, to some other weblog discussions inspired by Math is hard:

• Technicalities
• MathCog Idiocy

Math is hard. Discuss.

In the comments to this post, David MacIver provides an alternative, registration-free link to Tim Chow’s You Could Have Invented Spectral Sequences.

I poked around Tim Chow‘s site, and found two other interesting articles (in the form of old sci.math.research posts):

• Forcing for Dummies. Forcing is the technique invented by Paul Cohen to prove the independence of the Continuum Hypothesis.
• What is Class Field Theory? Class field theory describes the extensions of a field with abelian Galois group.

The American Mathematical Society produces, at great expense, Mathematical Reveiws, which provides a capsule summary of every paper published in a mathematics journal. Here’s something that just occurred to me today: does anyone actually use these reviews? I’ve used MR as a bibliography of papers by a particular author, but I can’t say I’ve ever read one of the reviews out of anything but idle curiousity. Does anyone else rely on this feature of MR?

Update. Apparently, it’s just me. I’ve been informed via email that everyone uses MR reviews.

The January Notices of the AMS is available. It features an article with the intriguing title You Could Have Invented Spectral Sequences.

Update. I’ve finally found the time to look at this article, and it is the simplest introduction to the subject I’ve ever seen. It acheives its simplicity by concentrating on the special case of the spectral sequence for filtered chain complexes.

Terence Tao has an interesting survey article out: The dichotomy between structure and randomness, arithmetic progressions, and the primes.

The latest issue of the Bulletin of the AMS of now available (though most of the articles have been available online for a while).