Category Archives: Mathematics

Ways to improve Mathematics (an introduction)

Posted on September 17, 2026 by Persiflage

The goal of this continuing sequence of posts is to recognize the reality in how our subject is changing and how we should adapt. Even in a hypothetical world where AI was infallible, essentially omniscient, benevolent, a wonderful expositor, and … Continue reading →

Posted in Mathematics | Tagged , , , , , , , | 10 Comments

Look, Mom, I pressed a button! (Go edition)

Posted on September 9, 2026 by Persiflage

Apropos of nothing, I was reminded recently of a fascinating story I heard from Geordie Williamson about AI and go — perhaps this story was the original source. It is a story about how a technology which has the power … Continue reading →

Posted in Mathematics | Tagged , , | 5 Comments

Look, Mom, I pressed a button!

Posted on September 5, 2026 by Persiflage

I have recently heard a few extraordinary opinions about how mathematicians should use AI. One I would paraphrase as “professional mathematicians should never use AI for any problem not in their narrowly defined (by whom?) research program”, which seems ridiculous … Continue reading →

Posted in AI, Mathematics | Tagged , , , , , , , | 11 Comments

OpenAI, updated

Posted on August 23, 2026 by Persiflage

An update on this post, from my inside sources: word on the math streets of SF is that the OpenAI team tried something like 500 problems to get their 10 solutions. I don’t know how much of an insider this … Continue reading →

Posted in Mathematics | Tagged , , | 6 Comments

The inverse Galois challenge, part II

Posted on August 16, 2026 by Persiflage

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 →

Posted in Mathematics | Tagged , , , , , , , , , , , , | 3 Comments

Putting ChatGPT through its paces

Posted on August 11, 2026 by Persiflage

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 →

Posted in Mathematics | Tagged , , , , , , , , , , , , , | 5 Comments

Observations from the ICM, Part 1

Posted on August 7, 2026 by Persiflage

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 →

Posted in Mathematics | Tagged , , , , , , , , , , , | 1 Comment

Look at everything that OpenAI failed to prove!

Posted on August 2, 2026 by Persiflage

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 →

Posted in Mathematics | Tagged , | 8 Comments

Xena on Counterexamples

Posted on July 22, 2026 by Persiflage

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 →

Posted in Mathematics | Tagged , , , , , , , , , , | 3 Comments

The moral panic over AI

Posted on May 26, 2026 by Persiflage

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 →

Posted in Mathematics | Tagged , , , | 2 Comments