MATHEMATICS
A New Proof of the Collatz Conjecture? Not Quite — But the Approach Is Genuinely Novel
A preprint claims significant progress on one of mathematics' most notorious open problems. The result falls short of a full proof, but the density arguments introduced may be the real contribution.
AI & MACHINE LEARNING
The Geometry of Large Language Models: Mathematicians Are Finally Making Sense of What's Inside
A new framework from algebraic topology is giving mathematicians precise language to describe the internal structure of neural networks — and the results are surprising.