Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...

Monstrous moonshine, a quirky pattern of the monster group in theoretical math, has a shadow - umbral moonshine. Mathematicians have now proved this insight, known as the Umbral Moonshine Conjecture, ...

The last dimension of Keller's conjecture has been proven using a computer algorithm. The conjecture involves the way hypercubes in different dimensions share sides when tiled. The proof is ...

This voice experience is generated by AI. Learn more. This voice experience is generated by AI. Learn more. News about AI math problem raises realization that finding counterexamples can be extremely ...

An OpenAI model disproved the 80-year-old Erdős unit distance conjecture, and Google DeepMind's AlphaProof Nexus solved nine more open problems days later. Together, these AI math breakthroughs mark a ...

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall. Summer Haag and Clyde ...