An OpenAI Model Solved a Famous Math Problem that Stumped Humans for 80 Years
OpenAI’s model found a grid-based construction that yields more unit distances by using Pythagorean pairs, including a 13×13 example with 12 neighbors.
- OpenAI solved the Erdős unit distance conjecture, revealing how grid spacing impacts the number of unit distances between points in a geometric arrangement.
- Erdős previously observed that adjusting grid spacing allows more points to intersect with unit circles, increasing potential distance pairs through diagonal configurations.
- The Pythagorean theorem guides this discovery, defining distance c between points using horizontal and vertical coordinates a and b to satisfy a² + b² = c².
- Choosing c² equals 25 allows the equation to be satisfied by grid points such as or , forming a circle of unit-distance neighbors.
- Scaling the grid down to 1/65 produces unit circles intersecting 16 grid points, demonstrating how OpenAI's AI refines complex geometric arrangements for broader mathematical significance.
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An OpenAI Model ‘Disproved’ a Famous Math Conjecture. This Mathematician Couldn't Leave It Alone
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.
An OpenAI model solved a famous math problem that stumped humans for 80 years
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 years. OpenAI gave several mathematicians early access to the result and published their reactions. Tim Gowers—who won the Fields Medal, the most prestigious prize in mathematics—wrote that “there is no doubt that the solution to the unit-distance prob…
A model of artificial intelligence developed by OpenAI solved a mathematical problem formulated almost 80 years ago and considered one of the important challenges in the field of discrete geometry. The result was verified by independent mathematicians, who confirmed the validity of the demonstration and described the achievement as a reference moment for the use of artificial intelligence in mathematical research.
Open AI says its artificial intelligence has cracked a puzzle that took top mathematicians 80 years to solve. Mathematicians are excited about the AI's capabilities.
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