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The Future of Research in the Age of AI
INRIA research scientist Pierre Marion sets out four working hypotheses about LLMs in math and computer science research, argues against both refusing LLMs and accelerating for its own sake, and sketches a middle path: use AI to multiply output while keeping skills sharp, verifying results formally, and putting training back at the heart of the PhD.
11 min · 2,464 words
Surprisingly Complex Waves Reveal the Brain's Inner Workings
Unexpected patterns traveling across the human brain may be reorganizing its activity in real time.
9 min · 2,113 words
Coltrane's Tone CircleExploring the circle of fifths, its jazz applications, and Coltrane's geometric approach to harmony
A clear walkthrough of John Coltrane’s famous tone-circle sketch: the circle of fifths, geometric harmony, and how jazz musicians still use the diagram today.
11 min · 2,485 words
Responsible Release of AI-Generated Mathematics
The Advisory Group on Mathematics and AI (Sep 29, 2026) recommends how frontier labs should release AI-generated math results: deposit promptly, cite related work, formalize where possible, disclose prompts and costs, and fund community-led human understanding.
2 min · 559 words
What's the Future for Pure Math Research in the Age of AI?
Stephen Wolfram surveys AI’s growing role in pure mathematics—headline ‘solved’ problems, what automation does and doesn’t replace, and how human mathematical taste and research programs may evolve.
31 min · 7,084 words
Burning Man Death Rates: A Short Lesson in Statistics
Summary: Three people died at Burning Man in 2026. This was about a quarter of what the crude national rate would predict (~12 deaths). Calculating the age-standardized death rate, we’d expect to see an average of 4.9 deaths. At this rate, seeing 3 deaths is not abnormal. However, Burning Man’s near zero death rate over its existence is abnormal, and likely due to selection bias of healthier attendees and other confounding demographic factors.
6 min · 1,389 words
A short note on the lunar terminator paradox: why the day/night boundary on the Moon looks sharper (or stranger) than everyday intuition about lighting predicts.
2 min · 529 words
Exploding variance of means of exponentials: least-squares to the rescue
Francis Bach reframes log-sum-exp / KL estimation as a continuum of least-squares problems with closed-form spectral solutions—cutting exploding exponential variance.
2 min · 464 words
L-systems generate weevils, pizza toppings, and matriarchal lineages
Mark Jason Dominus explores Fibonacci words and L-systems—how the same rewrite rules generate rabbit genealogies, weevil patterns, pizza toppings, and matriarchal lineages.
2 min · 360 words
How to win a beer with high-dimensional statistics
Jamie Simon explains a viral high-dimensional statistics paper with a bar-bet framing: why naive intuition about data geometry fails, and how the right summary wins the round.
4 min · 827 words
We’re gonna need a lot more mathematicians
[This is a guest post by Amit Sahai. This blog post was initially written in a different file format and converted using AI. — T.]
6 min · 1,318 words
Biology Might Not Be Quantum, but Its Math Is Quantumlike
Elise Cutts for Quanta Magazine explores how biological systems may not rely on quantum physics, yet often obey quantumlike mathematics—interference, contextuality, and what that means for modeling life.
11 min · 2,523 words
What Happens When Formalization Becomes Cheap?
I started working on machine learning for formal theorem proving in 2018. When people ask how I got into the field so early, I sometimes give an answer that makes me sound quite visionary. The actual story is that my advisor had a student leaving, and he assigned the project to me. My apologies to everyone who got the visionary version. It was a fortunate assignment. Over the following years, I developed CoqGym and LeanDojo and contributed to Goedel-Prover. I was lucky to join a small research…
13 min · 2,890 words
Announcing the Advisory Group on Mathematics and Artificial Intelligence
Nine leading mathematicians announce an independent IAS-hosted advisory group to counsel AI labs on releasing math results—starting with OpenAI’s claim of 100+ solved open problems—and invite community input.
2 min · 378 words
Why Do We Need Human Mathematicians Anymore?
This is a guest post by Po-Shen Loh, crossposted from his blog, where an illustrated version appears. This blog post was initially written in a different file format and converted using AI. — T. Similar logic applies to every industry and every job. And it comes to the conclusion that we won’t have enough people for all the jobs that need to be done. 100% of this post’s prose was written by Po-Shen Loh in a vim terminal, with no AI generation.
13 min · 2,959 words
It’s an egraph that supports well-scoped alpha aware binders. I made a tool that attaches my lifting e-graph ideas arxiv youtube to an s-expression based frontend. - repo https://github.com/philzook58/lambda-microegg - wasm demo https://www.philipzucker.com/lambda-microegg/ .
15 min · 3,440 words
Duality in Optimization: A Visual Tutorial
Mohini Bariya’s arXiv tutorial builds geometric intuition for Lagrangian duality in optimization—bridging solver techniques and solution interpretation with visual explanations of the dual.
1 min · 114 words
A Fractal Kitty rabbit-hole note on minimum L-seams: combinatorial geometry and puzzle-style constraints for tiling and seam placement, with worked intuition for curious math readers.
3 min · 786 words
Danielle Navarro warns against dplyr::ntile() in regulatory analyses: the SQL-inspired ranking helper often fails to produce equal-sized groups or the quantile splits analysts think they are getting.
29 min · 6,556 words
Arya Mazumdar on the existential panic among mathematicians after AI claimed a Millennium Prize problem, and why the field’s identity is more than automated proofs.
3 min · 684 words