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An essay on mathematicians' emotional reactions to AI-generated proofs, from Terence Tao's call for etiquette and Hugo Duminil-Copin's account of panic to spiritual angst and humility, set against the 1976 four color theorem and other industrializing disciplines, arguing the romantic era of mathematics is ending.
8 min · 1,738 words
How to Formalize All of Mathematics
A guest post by Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz. Responding to calls to formalize all of mathematics now that AI proves theorems well, the authors say a coordinated effort could expand discovery if done well but do lasting damage if rushed, and lay out their concerns and experiences with AI and formalization.
10 min · 2,382 words
The math that OpenAI keeps for itself
Daniel Paleka on what OpenAI's flood of AI-proved math results conspicuously skips—especially cryptography—and why the gaps matter for research priorities before the field's incentives shift further.
5 min · 1,192 words
Why are we even doing all this?A guest post on What’s new about the value of curiosity-driven work in an age of AI
Rikab Gambhir’s guest post on Terence Tao’s blog asks what research and learning are for when AI can already answer many technical questions—arguing for curiosity, taste, and the human practice of doing hard things even when tools get smarter.
6 min · 1,455 words
I Know Why the Mathematicians WeepOn technological grief
Derek Thompson talks with Cornell mathematician Steven Strogatz about why OpenAI's flood of AI-generated proofs has left mathematicians grieving, arguing that science is both a craft and a conversation between minds, and that machines producing knowledge without human understanding threaten the social half of science that people will need to protect.
8 min · 1,932 words
The 1st Time Machines Mogged Mathematicians
Pessimists Archive's Louis Anslow revisits the 1976 computer-assisted proof of the Four Color Theorem by Appel and Haken, the skepticism and outright rejection it drew from mathematicians, how acceptance slowly came, and the parallels with today's debate over AI-generated mathematics.
4 min · 979 words
A guest post on Terence Tao's blog by Kate Stange and Edmund Harriss reporting on an Institut Henri Poincaré workshop that asked what it would mean for a mathematical illustration to be rigorous, and reflecting on meaning, understanding and human practice in mathematics as AI and formal proof reshape the field.
9 min · 2,184 words
Who Taught the Machines Mathematics?
Nisheeth Vishnoi reflects on OpenAI releasing more than seven hundred AI-produced mathematical manuscripts: on the human knowledge these systems were built from, credit and attribution, and what becomes of mathematics as a human practice.
10 min · 2,194 words
What mathematicians should know about the Lean Theorem Prover: questions of reliability and AI
In a guest post on Terence Tao's blog, Thomas Hales explains how formal proof in the Lean theorem prover works, what can and cannot go wrong with its trusted kernel, axioms, definitions and autoformalized statements, and what mathematicians should check before trusting AI-assisted formal proofs.
16 min · 3,614 words
What should we tell our students?
In a guest post on Terence Tao's blog, mathematician Álvaro Lozano-Robledo addresses students worried by AI progress in mathematics: keep calm and carry on studying, because there is still much research, explanation and communication of mathematics to be done, with and without LLMs.
19 min · 4,466 words
OpenAI, the Partition Principle, and mathematics
Set theorist Asaf Karagila responds to OpenAI's claim about the Partition Principle and the Axiom of Choice: why he will not send Sam Altman whisky, what formalization still misses, and what the episode says about math, AI and publicity.
5 min · 1,182 words
Scott Aaronson reacts to OpenAI's release of 372 AI-generated mathematical results, including a claimed proof of the Unique Games Conjecture his wife Dana Moshkovitz worked on for years. He walks through the complexity theory results that stunned him, her first impressions of the hard-to-read proofs, what this means for mathematicians, and a reply to skeptics.
10 min · 2,293 words
In a guest post on Terence Tao's blog, Jeremy Avigad argues that AI is changing what it means to do mathematics, a shift with historical precedent, and reflects on what it means for how mathematicians work, what the community should value, and the norms it now needs to rebuild.
9 min · 2,068 words
Quo Vadis, Mathematics?Is Mathematics Over, or Just Graduating?
xAI co-founder Christian Szegedy asks whether mathematics is ending or graduating as AI automates theorem proving—drawing on Hungarian competition culture to argue AI will scale applied math as infrastructure while “high math” concentrates on deepest questions.
8 min · 1,877 words
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
Recent events in the field of AI for mathematics have shown us beyond all reasonable doubt that the field is currently undergoing a rapid transformation, unlike anything that we have ever seen before. Language models are solving hard problems which humans could not, and mathematicians are reacting very differently to this news. I personally am extremely excited about the future of our field. However it is becoming clear to me that my views are not shared by everyone in the community: indeed, many of my colleagues seem to be upset. So let me start by outlining my…
12 min · 2,857 words
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
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
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