Wired

‘Nasty’ Geometry Breaks a Decades-Old Tiling Conjecture

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 ...

‘hello there the jacobian conjecture is false thanx’: why a tiny social media post has mathematicians rethinking AI

Yet another longstanding mathematical question has been resolved by AI – and it feels a little different from the ones that ...
Phys.org

Mathematicians prove Pólya's conjecture for the eigenvalues of a disk, a 70-year-old math problem

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 ...
The Conversation

Millennium Prize: the Hodge Conjecture

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 ...
Nature

Conjuring with conjectures

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 ...
Wired

‘Nasty’ Geometry Breaks a Decades-Old Tiling Conjecture

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 ...