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, ...
Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal ...
OpenAI announced on May 20, 2026, that an internal general-purpose reasoning model had produced a counterexample to Paul Erdős's 1946 unit distance conjecture — a result in discrete geometry that had ...
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 ...
MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one results in a ...
OpenAI's AI helped overturn a longstanding math conjecture by finding a counterexample, highlighting a powerful new way to ...
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 ...
The Poincaré conjecture can be understood by analogy with the case in two dimensions. A two-dimensional space, or surface, is like a bubble made from an infinitely thin film of soap. If the bubble is ...
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