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 ...
As millions of people were coming down from the excitement of the FIFA World Cup Final at the start of this week, a different kind of excitement was building within the mathematical community. Levent ...
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 ...
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 ...
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 ...
An Anthropic researcher used the AI model Claude Fable 5 to find a counterexample. This discovery challenges the 87-year-old Jacobian conjecture in mathematics. The AI-assisted finding reportedly ...
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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