OpenAI makes breakthrough on 80-year-old maths problem

The Guardian reports on a significant advancement by OpenAI, the creators of ChatGPT, in tackling a complex mathematical challenge: the planar unit distance problem, first posed by Hungarian mathematician Paul Erdős in 1946. This development is framed as a notable step in AI reasoning, showcasing the technology's potential to contribute to fundamental scientific research. The article highlights how OpenAI's model challenged an 80-year-old conjecture, which proposed that the number of pairs of dots at the same distance apart on a sheet of paper would rise only slightly faster than the number of dots themselves.

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For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better.

From a UK perspective, as presented by The Guardian, this story emphasizes the intersection of cutting-edge technology and theoretical mathematics. The breakthrough is significant not just for AI development but also for the mathematical community, as it opens new avenues for exploration. The article carefully notes that while the AI has disproven the limit Erdős proposed, it hasn't provided a definitive answer to the rate of increase, indicating that human mathematicians remain crucial in the process. This nuanced reporting reflects a balanced view, celebrating the AI's capability while acknowledging the indispensable role of human intellect and collaboration.

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While the original proof produced by AI was completely valid, it was significantly improved by the human researchers at OpenAI and the many other mathematicians involved in the present paper. The human still plays a vital role in discussing, digesting and improving this proof, and exploring its consequences.

The involvement of mathematicians like Thomas Bloom and Tim Gowers, who co-authored papers and provided commentary, is crucial to the narrative. Their validation of OpenAI's work, especially after a previous claim by the company was debunked, adds credibility. Bloom's observation that the AI "persevered down paths that a human may have dismissed" is particularly insightful, suggesting that AI can augment human creativity by exploring exhaustive possibilities. Andrew Rogoyski's comment about AI providing "new ways to look at problems" and becoming a "fundamental tool of future scientific research" encapsulates the forward-looking perspective The Guardian often adopts on technological advancements. The story is presented as a milestone, underscoring the transformative potential of AI in fields previously considered exclusively human domains.

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a milestone in AI mathematics