One of the most prolific and interesting math bloggers and Twitters, John D. Cook (his blog is The Endeavor and he is @JohnDCook on Twitter) has been using Twitter in a very interesting way. In addition to his personal account, he has set up more than half a dozen daily Twitter messages on a variety of topics. (Apparently he composes most of the tweets in advance and has them posted automatically once a day, 7 days a week.)

Here are his daily mathematical Twitter accounts:

@AlgebraFact: a mixture of linear algebra, number theory, group theory, etc.

Example: If 2^p – 1 is prime, 2^{p-1}(2^p – 1) is an even perfect number. Euclid, Prob IX.36.

@ProbFact: theorems in probability, plus historical tidbits and applications.

Example: The mean of a Poisson random variable equals its variance. This can be a problem in applications. http://bit.ly/ijNfA

@AnalysisFact: facts from real and complex analysis (ranging from elementary to advanced).

Example: Complex conjugate maps x + iy to x – iy. This is not an analytic function.

@TopologyFact: Facts from topology and geometry

Example: The image of a compact set under a continuous function is compact.

@TeXtip: Tips for learning TeX and LaTeX (coming soon)

(He also has two other daily accounts: @RegexTip on regular expressions and @SansMouse on keyboard shortcuts in Windows.)