I thought I’d take a moment to introduce you to three math blogs I’ve recently discovered that don’t seem to be widely linked in the mathblogging community.
Annoying Precision (by t0rajir0u): This is the blog I would have written 8-10 years ago. I know nothing about the author, except that he or she is an MIT undergrad. The level is undergraduate, or very sophisticated high school, and the posts are consistently the very best material that can be studied at this level. T0rajir0u has a thorough understanding of how to use generating functions, calculus, linear algebra, finite fields and so forth and does a great job showing off their uses. Posts I particularly liked: The magic of the Frobenius map, Three approaches to sums of squares.
Gödel’s Lost Letter and P=NP (by RJ Lipton): RJ Lipton is a professor of computer science at Georgia Tech. He likes to take one particular mathematician or computer scientist and concentrate on that person’s impact on complexity theory. In these write ups, not only is the math very readable, but I get a great picture of how the work fits into the context of complexity as a whole. Posts I particularly liked: Bellman, Dynamic Programming, and Edit Distance, The Unbounded Power Of Randomness
XOR’s Hammer (by Michael O’Conner): Michael is a recent Ph. D, specializing in logic. His posts concentrate on applications of logic and set theory to fun problems in math and life. If you are tempting to think of logicians as abstract and disconnected from mathematical life, Michael’s blog is an excellent cure. Posts I particularly liked: What Happens When You Iterate Gödel’s Theorem?, How to Show that Games are Hard.