rare fail from @OpenAI -- i have to migrate all my custom-GPT course tutors to "plugins" so that people can continue to use them... but plugins are not publicly shareable. i've got thousands of students relying on these to help with their courses... custom GPTs were amazing...

am about to give a talk to the math dept @Penn on how to use AI to do math research. i did an experiment where i started 40 hours ago, fed claude/chat a half-dozen old unloved papers of mine on euler calculus, and had it generate new results / find hidden uses outside of math / build deeper connections in pure math. not bad! came out with three research directions, a half-dozen new potential applications, and a 10-page preprint of a geometric analysis result that looks to be solid after a few reads. oh, and claude took a few screenshots of slides from an old talk of mine and build a 60-slide powerpoint deck in my style with original images (!) and videos (!!). and we're getting better from here...

looks like I could get a job at the FBC...

math that you can do during the AI apocalypse... --- hopf fibrations ---

The status quo for R1 institutions cannot last. I'm guessing there will be a barbell distribution of focus that splits the classical research/teaching fusion we currently enjoy. A few OOM of improvement in AI and we might see: 1. The research side goes industrial -- applied mathematicians producing enormous bodies of interdisciplinary work; physical science labs running in warehouses with heavy robotics and automated data collection and processing; economics and social science simulations at extreme scales... 2. Teaching is top-quality, high-touch, personalized-service, with courses becoming works-of-art and top professors being superhuman performers and guides. In short, each end of the research-teaching axis taken to extremes. There are hints of this divergence already. At Penn, the two top schools (by $$$ & prestige) are the medical school (no undergraduate teaching; lots of heavy lab-based research at scale), and the business school (almost all teaching, highly profitable, most research occurring in pockets like the stats department at wharton). Ramp that split with AI improving 100-fold and more, and we will see a vast bimodal transformation that integrates the university more with industry (large scale research) and serves students better (extremely attentive teaching).

it's been 18 months since i was at an NSF workshop on math & AI. at that meeting, people were clamoring for "universal standards" on how AI should be used in math. i argued that they had no idea what AI in math would be capable of in a year. when i said that in the future, we would see people posting hundreds of papers per year to the arxiv, there were audible gasps of incredulity followed by proposals to limit the amount of work that one person could produce per year... and yet i still underestimated where we are now in terms of capabilities. (n.b., i'm not advocating for individuals publishing ~1 paper/day, but i am saying that this is likely to happen)

how to know the fall semester is in full swing: grading/writing exams while sick with a cold...

ok, so i've been practicing... now i can spin this the other way & the other way & the other way

Happy 200th birthday to Bernhard Riemann

/the young people are all right/ student newspaper at penn @dailypenn doing a great job debunking the latest "AI is going to kill us by 2030" psyop... thedp.com/article/2026/09/pe…

Elites are pessimistic about technological change because technological change changes who are elites

if the highest goal of mathematics was to achieve clear conceptual understanding of deep ideas, rather than solving important problems, then why is the fields medal the highest award? why is it that good expositors/writers are often considered "not serious"?

breaking: fields medalists agree to shake fists at sky

odd number of gears? need 'em to spin in a cycle? gotchu covered... (not sure an image/vid model can do this...)

Before @OpenAI announces the resolution of a Millennium Prize Problem, allow me a little mathematical flex 😎 With @Isaacramr__, we proved that a single ball in a 2D billiard can simulate a universal Turing machinesolving a problem posed by Cris Moore.🎱🤖 pnas.org/doi/10.1073/pnas.26…

in late 2024 i was using ai (gpt-o1) to make and prove conjectures; in 2025 i switched my math research to something so visually-dependent that i would be able to prove the work was not ai-based: visual paradoxes, which even the latest models struggle with...