A mathematical problem almost eighty years old, which until now resisted the greatest minds in the discipline, has just been solved by an artificial intelligence model developed by OpenAI. This advance surprised the scientific community which already describes it as a major turning point in the capabilities of AI applied to mathematics, summarizes New Scientist.
The news provoked particularly enthusiastic reactions among experts. Misha Rudnev, a mathematician at the University of Bristol, says he never expected to see such a breakthrough in his lifetime. According to him, this discovery is quite simply “explosive” and marks an extraordinary moment in the history of the discipline.
For his part, Tim Gowers, of the University of Cambridge, described this result as real “milestone in AI-assisted mathematics”. In a post accompanying the publication, he emphasizes that if a human had submitted such a demonstration to a prestigious journal, he would have accepted it without the slightest hesitation. He adds that no evidence generated by artificial intelligence has reached such a level until now.
The problem in question dates back to the 20th century and was formulated by the famous Hungarian mathematician Paul Erdős. Known for his major contributions, Paul Erdős considered this puzzle, called the problem of distinct distances, to be one of his most notable.
Simple question, complicated answer
The question asked is relatively simple to understand: on an infinite sheet of paper, if we place points in any configuration, how many segments of the same length can we trace between these points? Behind this accessible formulation lies a formidable mathematical challenge, which has withstood decades of research.
Paul Erdős had proposed a hypothesis according to which the optimal configurations would be those where the points were arranged in a grid. In this case, the maximum number of segments of equal length would only slightly exceed the total number of points. This intuition has guided research for decades.
However, despite many efforts, mathematicians have only managed to make marginal improvements to this conjecture. Attempts to either prove this upper limit or discover more efficient configurations have encountered persistent obstacles. The last significant advance was more than forty years ago.
The recent resolution by an AI is now a game-changer. It not only demonstrates the growing power of these systems in highly abstract domains, but also paves the way for new collaboration between humans and machines in mathematical research. This success could well herald a lasting transformation in the way in which major scientific puzzles will be tackled in the future.
