For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the planar unit distance problem. The question posed by the legendary Hungarian ...
In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 ...
After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved—via a straightforward query to a chatbot. “No previous AI-generated proof has come ...
Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...
An OpenAI model disproved the 80-year-old Erdős unit distance conjecture, and Google DeepMind's AlphaProof Nexus solved nine more open problems days later. Together, these AI math breakthroughs mark a ...
In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...
Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...
The following is an excerpt from The Gravity of Math: How Geometry Rules the Universe by Steve Nadis and Shing-Tung Yau. Copyright 2024. Available from Basic Books ...
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