Kevin Hartnett

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded.

Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.

A new paper finds a faster method for determining when two mathematical groups are the same.

Minhyong Kim is leading a new initiative called Mathematics for Humanity that encourages mathematicians to apply their skills to solving social problems.

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.

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

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.

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

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