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Formalizing the Enormous Theorem
Axiom releases the first complete computer-checked Lean proof of the Classification of Finite Simple Groups, the roughly 15,000-page 'enormous theorem'. Over 24 days, its engineers and mathematicians directed swarms of AI agents that produced about 43.1 million lines of Lean, surfacing 34 notable deviations from the published record and a new group theory result.
18 min · 4,183 words
A Fix for Softmax and Cross-Entropy
Jonathan T. Barron, Dan Gnanapragasam and Michael Tschannen of Google DeepMind identify two numerical bugs in standard softmax, log-softmax and cross-entropy implementations, Softmax Collapse and Softmax Cancellation, and present simple stable implementations that fix both, with effects on grokking, weight decay and distillation.
26 min · 5,999 words
Khalid Hamadeh shows that the 256-byte PITABLE in Ron Rivest’s RC2 cipher (RFC 2268), and a second unexplained table, are reproduced exactly by a Fisher–Yates shuffle driven by the decimal digits of π, three digits per draw, with code to verify it.
13 min · 2,954 words
This arXiv paper argues that Lean verification of AI autoformalised proofs gives no guarantee the original natural language argument is correct, because faithfully resolving ambiguity in mathematical text is harder than the Halting problem. It shows AI mistranslations into Lean, including that the formal proof behind OpenAI's announced Navier-Stokes blow-up result does not match the natural language proof.
1 min · 249 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
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
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
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
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