Almost a century ago, a mathematician came up with a puzzle that was so seemingly simple and yet so fiendishly difficult that it has been distracting other mathematicians ever since. It has become a ...

Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal model—and what that could mean for mathematics. Reading time 10 minutes Will ...

A new Physical Review Letters study places constraints on the ER = EPR conjecture, showing that under the authors' assumptions, the conjecture would imply possible alterations to the hyperfine ...

OpenAI announced on May 20, 2026, that an internal general-purpose reasoning model had produced a counterexample to Paul Erdős's 1946 unit distance conjecture — a result in discrete geometry that had ...

On May 20, 2026, OpenAI announced that its internal AI model had disproven a long-held prediction regarding the 'unit distance problem,' a central unsolved problem in discrete geometry. The unit ...

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...

The Collatz Conjecture is defined by a rule simple enough for a child to follow. No matter what number you start with, the process always appears to end the same way — and it has never been observed ...

The Collatz Conjecture begins with a simple sequence yet no proof has ever been found to solve it. Month’s worth of rain in a week coming for millions of Aussies Coffee linked to significant new side ...

When Hannah Cairo was 17 years old, she disproved the Mizohata-Takeuchi conjecture, a long-standing guess in the field of harmonic analysis about how waves behave on curved surfaces. The conjecture ...

Mathematicians have finally solved a geometry problem that has puzzled the field for decades. By wiggling a needle around while spinning it, you can minimize the amount of space it moves through, ...