An Old Conjecture Falls, Making Spheres a Lot More Complicated
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.
Elliptic Curves Yield Their Secrets in a New Number System
Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.
Computer Scientists Inch Closer to Major Algorithmic Goal
A new paper finds a faster method for determining when two mathematical groups are the same.
A Plan to Address the World’s Challenges With Math
Minhyong Kim is leading a new initiative called Mathematics for Humanity that encourages mathematicians to apply their skills to solving social problems.
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.
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.