An AI solution to an 80-year-old problem shocks mathematicians

In 1946, the Hungarian mathematician Paul Erdos posed a mathematical problem that mathematicians have not solved to this day. What humans have failed to achieve so far, AI appears to have achieved.

The problem of unit distance in the plane – also known as “Erdos Problem 90” – has fascinated mathematicians for decades. A universal AI model, and not a system specifically tailored to mathematics, has now found a solution to this.

Canadian mathematician Daniel Litt called it “the first result produced autonomously by an AI, which I find interesting in itself.”

AI solution enabled other solutions

Just a few days after the publication of the OpenAI paper, according to The Conversation, US mathematician Will Sawin followed the same chain of thought and came to an even better result. Additionally, last week, a Google DeepMind team used one of its own models to resolve nine other smaller open issues left by Erdos.

Paul Erdos was one of the most productive mathematicians of the 20th century. He was famous for asking seemingly simple questions whose solutions withstood decades of research.

For decades, square grids were considered the optimal solution

At first glance, the underlying problem seems relatively simple: Imagine a certain number of points – let’s call this number *n* – drawn on an infinitely large piece of paper. Assuming that the points can be arranged arbitrarily: How many pairs of points can be positioned so that their distance from each other is exactly one unit?

For decades there was a widespread belief that the highly regular structures of a square grid represented the optimum. Erdos also shared this theory.

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Top mathematician praises the AI ​​result

For the past 80 years, mathematicians have tried to either prove or disprove Erdos’ conjecture. However, OpenAI’s recent breakthrough contradicted Erdos’ intuition. The AI ​​used tools from a branch of mathematics – algebraic number theory – to show that for infinite values ​​of *n* there are dot patterns that have far more unit-spaced pairs than the square grid.

In an article that OpenAI published alongside the new specialist publication, several leading mathematicians commented on the result.

The Fields Medalist Timothy Gowers wrote that if a human researcher had submitted this work with the present results to the renowned journal *Annals of Mathematics*, he would have recommended its publication “without any hesitation.” He also noted that no evidence previously created by an AI has come close to this level of sophistication. In this case, the math world is looking enthusiastically at AI.