Matt Baker's Math Blog

“Let me explain.

Every time I’ve organized my thoughts sufficiently to finally write a proper blog post about the impact of AI on mathematical research, something massive happens which causes me to delay.

I’m on the Editorial Board of a highly non-traditional new journal called Mathematical Discourse.

My coauthors June Huh, Mario Kummer, Oliver Lorscheid, and I just posted a paper called Lorentzian polynomials and matroids over triangular hyperfields, Part 2: Analytic aspects on the arXiv preprint server.

Nine years ago, I wrote a July 4th blog post about matroids called A Celebration of Independence.

In celebration of Pi Day 2024, I would like to explain how the “Arithmetic-Geometric Mean” of Gauss and Legendre can be used to give a rapid method for computing the digits of .

A torsor (or principal homogeneous space) is, informally speaking, a mathematical structure quite similar to a group, but without a natural identity element.

In honor of Pi Day 2023, I’d like to discuss Hilbert’s 7th Problem, which in an oversimplified (and rather vague) form asks: under what circumstances can a transcendental function take algebraic values at algebraic points?

Test your intuition: is the following true or false?

In my previous post, I presented a proof of the existence portion of the structure theorem for finitely generated modules over a PID based on the Smith Normal Form of a matrix.

I’m teaching Graduate Algebra this semester, and I wanted to record here the proof I gave in class of the (existence part of the) structure theorem for finitely generated modules over a PID.