Mathematics

The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation.

For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that model semiconductors. A new method could change that.

After finding the homeschooling life confining, the teen petitioned her way into a graduate class at Berkeley, where she ended up disproving a 40-year-old conjecture.

Fan Chung, who has an Erdős number of 1, discusses the importance of connection — both human and mathematical.

A team of mathematicians based in Vienna is developing tools to extend the scope of general relativity.

After just a few months of work, a complete newcomer to the world of sphere packing has solved one of its biggest open problems.

Maria Chudnovsky reflects on her journey in graph theory, her groundbreaking solution to the long-standing perfect graph problem, and the unexpected ways this abstract field intersects with everyday life.

A tetrahedron is the simplest Platonic solid. Mathematicians have now made one that’s stable only on one side, confirming a decades-old conjecture.

Two new notions of infinity challenge a long-standing plan to define the mathematical universe.