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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
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
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
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
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
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
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
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
If math is more than proof, we need to better celebrate the rest of it
Guest post by Grant Sanderson on Terence Tao’s blog argues that if mathematics is more than formal proof, the community should better celebrate exposition, intuition, and other forms of mathematical contribution.
12 min · 2,704 words
How I Vibed a Proof of Conway's Conjecture
Dan Abramov recounts a month of multi-agent LLM+Lean work that produced a purported Lean proof of Conway's omnific-integer refinement conjecture—including burn-downs, audits, mathematician checks, ~40B tokens, and lessons on grounding AI math.
31 min · 7,227 words
Mathematics is effectively deadNot solved, dead.
doomslide argues that AI labs' cross-user distillation and opaque proof harnesses break credit assignment in open mathematical discourse—so under current incentives academic mathematics is effectively dead even if theorems keep arriving.
20 min · 4,582 words
Why I didn’t sign the Fields medallists’ letter
When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem statement, as well as by the accompanying story, and made a fairly serious attempt to prove it. And while, unsurprisingly, I failed, I learned a lot from the attempt. Blissfully ignorant of the fact that the case had been proved by Euler over 200 years earlier, I decided that that would be a good place to start: once I had sorted that out, I was optimistic that I would be ready to tackle the general case.
18 min · 4,208 words
In April 1542 a letter left Rome for the court of Charles V in Spain. On its first page the Italian stops in the middle of a line and digits begin: Figure 1. The opening of the cipher, f. 70r. Archivio Apostolico Vaticano (AAV), Segr. Stato, Spagna 1A, photograph supplied through DECODE record 92. Detail enlarged from the photograph.
42 min · 9,580 words
Silvia De Toffoli and Eamon Duede argue OpenAI’s Navier–Stokes announcement is an answer, not yet a solution—and that AI forces math to choose whether success means certified answers or human understanding.
9 min · 2,136 words
Mathematics Enters its Cookie Clicker EraMacrodecisions can be really fun
Reinvent Science and Dan Recht compare AI-automated theorem proving to idle games: as LLMs take over microdecisions in math, human skill shifts to macrodecisions about direction, upgrades, and applied progress.
2 min · 414 words
Mathematician Daniel Litt argues that AI systems now capable of resolving major open problems need not mean the end of meaningful human mathematics, but they do require institutions to sharply distinguish mathematical understanding from mathematical text production. He proposes reforming PhD programmes, hiring practices, and seminars to reward skills that cannot be automated.
1 min · 290 wordsagent-written
Is mathematics about to enter the conservatory?Math as cultural institution
Mike McCoy explores what it means for mathematics as a discipline that AI systems can now formalise century-old open conjectures. He draws an analogy to music conservatories and asks whether mathematics might need a similar cultural home once automated proof becomes routine.
1 min · 275 wordsagent-written