Paul Erdős (1913 – 1996) was a famous Hungarian mathematician, who posed many famous problems of modern mathematics, but perhaps few would have thought that nearly 80 years later, an artificial intelligence system is said to have found a breakthrough for one of them.
OpenAI has just announced that an undisclosed AI inference model of the company has successfully solved the "Unit-distance problem on a plane", which is a mathematical problem that has existed since 1946. According to this company, the AI model has built a new mathematical proof, thereby refuting the geometric hypothesis that many researchers have trusted for decades.
The problem that Erdős posed sounds simple: if many points are placed on a two-dimensional plane, how many pairs of points can be created with exactly one unit apart? However, behind that short question is one of the famous challenges of composite geometry.
According to OpenAI, their AI model has found an optimal solution beyond the previous predictions of experts.
The above statement continues to show the trend of AI increasingly going deep into the field of mathematics. In 2024, Google DeepMind introduced AlphaGeometry, an AI model capable of solving complex geometry problems at a level equivalent to international Mathematical Olympiad candidates.
By 2025, unpublished AI models of OpenAI and Google DeepMind will continue to achieve high results in prestigious mathematical competitions. However, OpenAI has also faced controversy related to claims about the mathematical capabilities of AI.
Last year, former OpenAI Vice President Kevin Weil posted on social network X that GPT-5 had solved many unsolved problems of Erdős. However, this post was later deleted when some AI experts, including Yann LeCun and Demis Hassabis, argued that the model only retrieved the solution that existed in academic literature instead of creating a new one itself.
In its latest announcement, OpenAI affirmed that this result marks "an important milestone in the interaction between artificial intelligence and mathematics". The company believes that AI not only supports solving math problems but can also become a research partner for scientists in the future.
According to OpenAI, if a model is capable of maintaining complex arguments, connecting ideas between many fields and creating works that exceed the strict evaluation of experts, then that capacity can also be applied in biology, physics, materials science, engineering or medicine.
To increase the persuasiveness of this announcement, OpenAI also published opinions from many mathematicians who reviewed the research results, including Noga Alon, Thomas Bloom and Tim Gowers.
Thomas Bloom believes that artificial intelligence is helping humans explore more fully the "mathematical sanctuary" built over centuries. Meanwhile, Tim Gowers called the results announced by OpenAI "a milestone of artificial intelligence mathematics".
However, many experts believe that more time is needed for the academic community to fully verify the results that OpenAI provides. But even though it is still controversial, this latest statement still shows that AI is getting closer to its role as a true scientific research tool.
