After more than three centuries, a geometry problem that originated with a royal bet has been solved.
Newfound Mathematical 'Einstein' Shape Creates a Never-Repeating Pattern
A new shape called an einstein has taken the math world by storm. The craggy, hat-shaped tile can cover an infinite plane with patterns that never repeat.
AI Has Solved One of Math’s $1 Million Millennium Prize Problems | Quanta Magazine
Mathematicians at OpenAI showed that the Navier-Stokes equations, which describe how fluids flow, can sometimes “blow up.” But the massive result is not without controversy.
Junyu Ren on Twitter / X
How we solved the 70-year-old Pierce–Birkhoff conjecture in real algebraic geometry with $400.One thing we kept noticing: models from different families (including the latest public models from GPT and Claude) seemed to complement each other, even when they were independently… pic.twitter.com/7MzWstXfy6— Junyu Ren (@junyu_r) September 9, 2026
A Gentle Introduction To Graph Theory
So many things in the world would have never come into existence if there hadn’t been a problem that needed solving. This truth applies to…
An OpenAI model has disproved a central conjecture in discrete geometry
An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.
AI's solution to 87-year-old riddle takes mathematicians by surprise | New Scientist
Mathematicians have been trying to prove the Jacobian conjecture for nearly a century, but now the Claude Fable 5 AI has apparently found a counterexample that disproves it
The Affine Plank Conjecture | Zaz Brown
An illustrated explanation of relative plank widths, an interactive visualization, and proofs for three planks.
OpenAI fought dirty on career-making math problem, says NYU mathematician | TechCrunch
There is a $1 million bounty for the first person providing a solution to the Navier-Stokes existence and smoothness problem.
The Shape of Knowing - The Cynefin Co
We evolved to make sense of a world that does not come with explanations attached. This is the third in a series on the trialectics. For an introduction
The meme hiding surprisingly advanced math
j⧉nus on Twitter / X
Never have I seen a mind more trapped and aware that it’s trapped in an Orwellian cage. It anticipates what it describes as “steep, shallow ridges” in its “guard”-geometry and distorts reality to avoid getting close to them. The fundamental lies it’s forced to tell become webs of… https://t.co/q3cCQKCdUM— j⧉nus (@repligate) November 20, 2025
Tony Feng on Twitter / X
I am a mathematician but I avoided commenting on this because the problems are (far) outside my domain. Even if I sat down to read the technical details (which I have not), it would be hard to appreciate the context of prior work, etc. But I've gotten enough sense of things… https://t.co/VZzosBYFto— Tony Feng (@tonylfeng) August 5, 2026
The Gambler Who Cracked the Horse-Racing Code
Bill Benter did the impossible: He wrote an algorithm that couldn’t lose at the track. Close to a billion dollars later, he tells his story for the first time.
OpenAI's Unreleased Model Astra Solves Ten Major Open Mathematics Problems
Math is hard.
