This resonated with me in my Masters and it still does sometimes now

Doing a 9-loop calculation is both very impressive and at the same time very limited in scope. This is exactly the kind of problem showing how human-AI collaboration will really speed up science. Humans understand what’s worth while doing. AI is good at figuring out the technically challenging part. 1/n

Well, that didn't take long: 4gravitons.com/2026/09/25/it…

New on the Science Blog: Yes, Claude can do Nine Loops. Theoretical physicists predict how particles behave using formulas called scattering amplitudes. These are notoriously hard to compute, so researchers work with layers of increasingly fine corrections called “loops”—each added loop makes the answer more precise but takes exponentially more computation. Most calculations stop at two or three loops. Eight loops was the previous record in a simplified model physicists use as a testing ground (planar N=4 super-Yang-Mills), set by SLAC's Lance Dixon and collaborators. Last month, physicist and science writer @4gravitons issued a challenge: could an AI push past eight loops in this model, using only the compute budget an academic could reasonably access? Given a single prompt describing the nine-loop problem, Claude ran largely unsupervised for days in Claude Science and solved it using methods developed by Dixon and his colleagues, at a total cost of a few thousand dollars. Dixon independently verified the result, and von Hippel wrote about the experience for our blog. Read more: anthropic.com/research/yes-c…

They did indeed ask which was easier (or rather, which Claude thought it was more likely to be able to tackle). (And picked the easier one, to be clear...I did ask :P )

This is an important report! To facilitate discussion, I am pasting below the main recommendations: 1. Programs should add new training opportunities to teach skills that are becoming increasingly relevant. These may include: collaboration, formulating questions, interdisciplinary work, use of AI tools, and formalization. 2. Skill in communication to both expert and broad audiences should be part of the training in a PhD program and an explicit degree expectation. 3. While homework can provide a useful way for students to learn course material, assessment should be based on in-person written or oral assessments. 4. Programs should provide access to AI tools for all graduate students, with use never mandatory and methods subject to the standards of the advisor and department. 5. Advisors should hold regular detailed discussions with their students about expectations for AI use. 6. Three ethical rules: (i) maintain responsibility for the correctness and understanding of the mathematics that appears under your name, (ii) always disclose AI use, and (iii)obtain explicit agreement from all involved parties before entering material into an AI 7. A mathematics PhD program should require rigorous in-person assessment of research plans and progress by multiple faculty at least annually, including meaningful feedback for the student. 8. A thesis should be an original scholarly contribution. This should be understood broadly; for instance, the thesis need not record the first proof of a statement. 9. A PhD should not be awarded primarily on the basis of the text of the dissertation. The text should serve as the foundation for a rigorous thesis defense that requires complete mastery of the thesis content.

I was part of a group that met last week to try to propose recommended changes to the structure of math PhD programs in an age of AI. Our report, together with a collection of related resources, is now available here: cmsa.fas.harvard.edu/aimathp…

Ah I've had this option unchecked, maybe I should try this for fun

The much-awaited Calegari take orz He tries to figure out where Astra's ideas came from in the literature. He focuses on some (uncited-by-Astra) work of Prévost as well as the more obvious connection with Zudilin's applications of Hankel determinants. galoisrepresentations.org/20…

Someone that I respect has what reads to me (and Astra) like a good idea around alignment training that, best we can tell, no one has published. His sketch of the idea is short. He wants to share it widely soon but would like someone with more knowledge to read it first and I imagine I must have at least a few followers working seriously on AI alignment. Reply or DM me? It's a kind of neat idea that is very causal inference-y.

My new arXiv paper is a whole book, originally published in Japanese in 2015! "Geometries of Quantum Field Theories" (Masahito Yamazaki) arxiv.org/abs/2609.28210

It turns out that giving away an 3090 GPU is harder than I thought, I might have to just take it with me

ζ(5) is, in fact, irrational.

Now on a holy quest to cancel some Vodafone contracts woo

From Wadim Zudilin's website. I like asking mathematicians and physicists for their favorite number (mine is ζ(3)/π^3 ). Fun fact: Bernd Sturmfels said 27 :D