Galois Representations and more!
This is a sequence to this post. The SAIR competition (Round I) has been completed! 98.4% of the possible signatures were obtained, with only 39 non-solvable cases missing. Some thoughts. First, my timing in the last post of dissing the Continue reading
We are all aware of what ChatGPT can do. I think we would be better informed if we also learn what it cannot do (at least right now!). In order to better understand the current capability of the latest publicly Continue reading
My recent post generated a surprising amount of personal emails defending of Philadelphia. I can happily report that, although I didn t really get a chance to explore the city in any depth, it has at least one excellent cafe. “Thank Continue reading
I was heartened to see a recent list of results proved by OpenAI here. Heartened because we are now clearly in an age in which AI can truly contribute to serious research mathematics. But also heartened because one can only Continue reading
There is an interesting post here on Xena s blog. I don t centre “proof” in mathematics to anywhere near the extent that Kevin does, but I think emphasizing that distinction obscures the fact that our opinions about mathematics, mathematicians, and, I Continue reading
I learnt a few days ago about the following AI challenge: find polynomials with Galois group \(G\) for each of the transitive subgroups of \(S_{24}\), with each of the possible signatures \((r_1,r_2)\) with \(r_1 + 2r_2 = 24\) where \(r_1\) Continue reading
A number of journals appear to have frothed themselves into a moral panic over AI. There is certainly a lot of AI-generated crap appearing in multiple places, and the arXiv moderators are no doubt playing whack-a-mole trying to keep it Continue reading
With the arXiv s new policies for posting, I am now getting inundated with requests from cranks for endorsements. Here is my suggestion for the arXiv: when someone requests an endorsement, there should be an option (rather than ignoring the email) Continue reading
Here are some memories about Dick Gross, who sadly just passed away very recently. Nothing was quite as reassuring as having Dick Gross in your audience. Inevitably, when your talk was done, he would both compliment you on it and Continue reading
The April 2026 Oberwolfach Arbeitsgemeinschaft will be on Arithmetic Holonomy Bounds and Applications to Irrationality, and in particular will discuss some of the results of this paper. For those who don t know, the Arbeitsgemeinschaft ( study group ) is different from usual Continue reading