An AI Breakthrough Just Solved An 80-Year-Old Math Problem — And Proved Humans Wrong

Since 1946, mathematicians have struggled to answer what seems, on the surface, to be a fairly simple question: How can you arrange an arbitrary number of points on a 2D plane to maximize the number of pairs that are exactly one unit apart? Traditional approaches have typically focused on grid-based layouts, but in May 2026, OpenAI claimed that one of its general-purpose reasoning models had disproven assumptions about this problem that have held for 80 years.

Previously, many mathematicians, including the problem's creator, Paul Erdős, believed that creating a grid of points with carefully chosen spacing was the optimum strategy. The problem is that the number of pairs was constrained by the size of the grid itself. In simple terms, OpenAI's model used advanced algebraic number theory to find a way to arrange points that resulted in a significantly higher number of valid pairs. It's important to recognize that this problem is not yet "solved," as there's no way to definitively identify the maximum pair count for any number of points.

The response from experts has generally been optimistic. Melanie Matchett Wood, professor of mathematics at Harvard University, noted that the mere existence of this new proof may garner the problem increased attention, which could lead to even further progress.

It's been proven that AI systems have the potential to benefit humanity, for instance by helping detect and diagnose cancer. As such, it is entirely possible that an artificial intelligence has contributed to a genuine mathematical breakthrough. That said, until human experts have had enough time to properly challenge and test the proof, it (and all other claims from AI companies) should be treated with a healthy degree of skepticism.

That's because running an AI company is expensive, and as such, OpenAI has a vested interest in making people believe its models are capable of extraordinary things. For instance, it has previously claimed to have solved 10 other Erdős problems, when in reality, the model simply found existing solutions in other people's work.

While still impressive, this is a significant downgrade from what was claimed and a reminder that LLMs generate profit by plagiarizing the hard work of humans on an industrial scale. It also helps illustrate why even AI experts don't trust chatbots — they don't actually understand the words they're saying, so when they're trusted blindly or given too much influence over important matters, there can be serious repercussions. Just ask the U.S. military, who recently learned the hard way after a chatbot nearly started a war by providing hallucinated intel about a ship's cargo.