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 ...
OfficeChai

OpenAI Proves The Rational Hodge Conjecture For CM Abelian Varieties: Understand What This Means

OpenAI has published a paper claiming a proof of the rational Hodge conjecture for a special but important class of geometric ...
Phys.org

40-year math mystery and four generations of figuring: Proof of Kelmans-Seymour Conjecture in Graph Theory

This may sound like a familiar kind of riddle: How many brilliant mathematicians does it take to come up with and prove the Kelmans-Seymour Conjecture? But the answer is no joke, because arriving at ...
OfficeChai

OpenAI Releases AI-Generated Proofs Of Quasi Riemann Hypothesis, Unique Games Conjecture & Hodge Conjecture For CM Abelian Varieties

We might be in the math singularity. OpenAI has released 722 AI-written math manuscripts, and CEO Sam Altman has picked out ...
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 ...
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 ...