A statement can be true or false. But as Kurt Gödel demonstrated, there will always be mathematical assumptions that can ...

My wife said she wanted “unique flooring,” which apparently meant I needed to spend days cutting plywood into geometric patterns like a sleep-deprived carpenter with access to power tools. Halfway ...

OpenAI announced this week that one of its general-purpose reasoning models made a breakthrough that has grabbed the ...

OpenAI says an AI reasoning model disproved an 80-year-old Erdős geometry conjecture, raising new questions about AI’s role ...

An AI system developed by OpenAI has produced a verified proof addressing a classic problem in discrete geometry first posed ...

Artificial intelligence built by OpenAI has cracked a decades-old conjecture by Paul Erdős, which mathematicians have hailed ...

OpenAI is claiming its internal general-purpose reasoning model may have disproved the Erdős unit distance conjecture, a longstanding question in discrete geometry. Outside review is central to that ...

OpenAI has revealed a breakthrough proof that overturns a nearly 80-year-old geometry conjecture posed by Paul Erdős.

OpenAI claims its reasoning model disproved a geometry conjecture unsolved since 1946 — and this time, the mathematicians who ...

By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far ...

Scientists have discovered that the Chinese money plant hides a remarkable geometric system inside its leaves, revealing that ...

Looking at a globe, a country’s coastline may appear smooth and continuous. But zoom in with a satellite view and that neat boundary dissolves as you see a maze of coves, cliffs, and peninsulas.