## Latest Articles

### The Number 15 Describes the Secret Limit of an Infinite Grid

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

### A New Symmetry Shakes Up Physics

So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.

### To Teach Computers Math, Researchers Merge AI Approaches

Large language models still struggle with basic reasoning tasks. Two new papers that apply machine learning to math provide a blueprint for how that could change.

### Google Researcher, Long Out of Math, Cracks Problem About Sets

On nights and weekends, Justin Gilmer attacked an old question in pure math using the tools of information theory.

### The Brain Uses Calculus to Control Fast Movements

Researchers discover that to sharpen its control over precision maneuvers, the brain uses comparisons between control signals — not the signals themselves.

### How Shannon Entropy Imposes Fundamental Limits on Communication

What’s a message, really? Claude Shannon recognized that the elemental ingredient is surprise.

### A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special

The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

### Special Surfaces Remain Distinct in Four Dimensions

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

### Mathematicians Clear Hurdle in Quest to Decode Primes

Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.