One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...
On the morning of October 7, the news that OpenAI had released 722 mathematical manuscripts featured headlines such as ...
Is it possible to deduce the shape of a drum from the sounds it makes? This is the kind of question that Iosif Polterovich, a professor in the Department of Mathematics and Statistics at Université de ...
Carnegie Mellon University computer scientists and mathematicians have resolved the last, stubborn piece of Keller's conjecture, a geometry problem that scientists have puzzled over for 90 years. By ...
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Chinese AI model helps prove 31-year-old math conjecture with machine-verified Lean proof
Chinese AI math proof reaches a new milestone: Shanghai AI Lab's Shusheng-S2 helped resolve the 31-year-old Ghys conjecture, ...
Microsoft Research announced on October 21, 2026 that Xinzhi Zhang, a senior researcher in its Machine Learning and Optimization group, and collaborator Zhao Song have proved the ...
The total amount of money invested in the project. The total cost includes EU contribution as well as other project costs not covered by EU funding. It is expressed in euros. Amount of money, by way ...
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 ...
They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...
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