A Ten-Year-Old Video about Larry Guth and Netz Katz.

Facebook recently reminded of a videotaped lecture I gave ten years ago on Larry Guth and Nets Katz. In that lecture, I discussed their famous joint work on the Erdős distinct distances problem, as well as some of their individual contributions.

Many of the problems mentioned there—relating to the Kakeya problem, the Navier–Stokes equations, systolic inequalities, quantum error-correcting codes, and sum–product theorems—have led to fascinating research over the past decade. Alex Lubotzky and Noam Solomon also made short but forceful guest appearances in the video.

From the news

A few days ago my, wife showed me an article (in Hebrew) reporting a startling new development in mathematics and asked whether I knew about the result and the two mathematicians involved.

I did not recognize either of the two mathematicians from the accompanying picture, nor could I immediately identify the mathematical problem they were studying. But once I read the text, things became clearer: the reported progress concerned the Riemann Hypothesis, and the two mathematicians were Larry Guth and James Maynard—both of whom I know quite well (or at least, I thought I did).

Still, they looked rather different from how I remembered them, and I could not tell who was who. A bit of further investigation resolved the puzzle: the image was AI-generated picture of two mathematicians discussing a mathematical problem. Apparently, in the age of AI, mathematical breakthroughs are still achieved by real people—but their photographs are optional.

AI and mathematics

I recently asked on MathOverflow about AI applications in mathematics and received interesting answers.