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Everything filed under Mathematics, newest first.
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Great Dirhombicosidodecahedron
| | Great Dirhombicosidodecahedron ("Miller's Monster") | - Vertex description: (5/2.4.3.4.5/3.4.3/2.4)/2 - Faces: 124 (24 pentagrams, 40 triangles, 60 squares) - Edges: 240 - Vertices: 60 - External facelets: 1280 - Dual: Great Dirhombicosidodecacron This model has 1280 external facelets to put together! The polyhedron is uniform, so all the faces are regular although it's hard to make them all out. It is the only uniform polyhedron with as many as 8 faces meeting at each vertex (two purple pen
2 min · 471 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
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
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
Stephen A. Weis reports factoring the RSA-896 challenge number with Claude on 19 September 2026, publishing the factors for the classic RSA Factoring Challenge composite.
1 min · 35 words
Mathematicians Build Long-Awaited Graph SandwichThe proof of a decades-old conjecture has given researchers a new way to understand complex networks.
Paulina Rowińska explains how Behague, Iľkovič, and Montgomery completed Kim and Vu's sandwich conjecture, letting hard properties of random regular graphs follow from easier binomial-graph results.
7 min · 1,621 words