OpenAI: An AI Solves an 80-Year-Old Math Problem

A Major Breakthrough by OpenAI

OpenAI's artificial intelligence model has recently achieved a significant breakthrough by solving a mathematical problem that has stumped researchers for 80 years. This challenge, posed by Hungarian mathematician Paul Erdős, involved determining the maximum number of pairs of points that can be placed at a distance of 1 on a flat surface. Until now, the scientific community believed that grid constructions were the optimal method for maximizing these pairs of points.

However, the new solution proposed by OpenAI's AI has proven this assumption to be incorrect. This discovery represents a crucial milestone for both the mathematical and artificial intelligence communities. According to OpenAI, this is the first time a major open problem in a subfield of mathematics has been autonomously solved by an AI. The creator of ChatGPT emphasized that this demonstrates the depth of reasoning these systems are now capable of.

A Generalist AI Model at Work

What makes this discovery even more impressive is that it was achieved by a generalist AI model from OpenAI, rather than a technology specifically optimized for mathematics. The model was tested with the problems posed by Erdős, and its results were validated by external mathematicians. These experts subsequently authored a scientific paper to explain the proof.

This cautious approach contrasts with a previous announcement from OpenAI, where an official claimed that GPT-5 had solved several of Erdős's problems, which turned out to be inaccurate. This time, validation by specialists, including researcher Thomas Bloom, lends greater credibility to this advancement. Bloom described this achievement as the "most impressive" in the field of mathematics by an AI to date.

Validation and Recognition

OpenAI took care to have the results verified by external experts before making this discovery public. The previous year, a premature announcement had led to criticism from prominent figures like Yann LeCun and the head of Google DeepMind. Today, the validation by specialists such as Thomas Bloom, who runs a site dedicated to Erdős's problems, reinforces the credibility of this breakthrough. Bloom stated on X that this is undoubtedly the most impressive achievement of AI in mathematics to date.

Implications for the Future

The resolution of this problem by a generalist AI underscores the potential of these technologies to transform scientific research. By challenging beliefs that have been established for decades, this discovery could open new avenues in the study of mathematics and beyond. It also illustrates how artificial intelligence can contribute to fields traditionally dominated by human expertise.