OpenAI makes breakthrough on 80-year-old maths problem | OpenAI
OpenAI has claimed to have made further progress in AI logic after its technology successfully solved an 80-year-old mathematical problem.
The company behind ChatGPT said it had made a breakthrough with a challenge first posed by Hungarian mathematician Paul Erdős in 1946: the planar unit distance problem.
The question posed by Erdős is simple to explain. If you take a piece of paper and add a few dots, how many pairs can there be at the same distance from each other? Erdős suggested that the number would increase only slightly faster than the number of points.
OpenAI’s model came to a different conclusion, drawing on different branches of mathematics to reveal a set of arrangements that exceed the limits of Erdős’s hypothesis.
“For almost 80 years, mathematicians believed that the best possible solutions looked roughly like square grids,” OpenAI wrote in X. “Now an OpenAI model has disproved this belief by discovering a completely new family of structures that perform better.”
Although the study excited mathematicians, the broader problem remains unresolved because the AI did not find a new answer to how fast pairs of dots rise, only showing that the limit Erdős suggested was too low.
OpenAI, which is preparing to list on the US stock exchange, said that calculations are made with a general-purpose reasoning model that breaks problems into smaller steps, rather than a system specifically trained for mathematics.
The initiative had been thwarted before by Erdős’ attempts to solve his problems; last year touted a so-called breakthrough based on existing literature that had actually been adopted by the model. This time, OpenAI’s work was confirmed by mathematicians, including mathematician Thomas Bloom. Erdö’s problems He criticized the website and OpenAI’s previous Erdős claims.
Bloom co-wrote a companion article to OpenAI’s blog post pointing out Erdős’ success. Bloom wrote that the AI system achieves its conclusions by “insisting on paths that a human might dismiss as not worth the time to explore.”
However, he added that humans are also involved in the work of artificial intelligence.
“While the original evidence generated by the AI is completely valid, it has been significantly improved by human researchers at OpenAI and many other mathematicians featured in this paper. Humans still play a vital role in discussing, digesting, improving and exploring the implications of this evidence,” he wrote.
Mathematician Tim Gowers, also writing in the companion article, called the result “a turning point in the mathematics of AI.”
Andrew Rogoyski, from the University of Surrey’s Institute for Human-Centered Artificial Intelligence, said the announcement showed that AIs were offering humans new ways of looking at problems.
“It is becoming clear that artificial intelligence is influencing the world of creative thought and will be a fundamental tool of future scientific research,” he said.
