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, ...
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 ...
Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal ...
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 ...
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 ...
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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