San Francisco — For decades, elite mathematicians have struggled to solve a set of thorny problems posed by a 20th-century academic named Paul Erdős.
This month, an artificial intelligence startup called Harmonic entered the fray. Harmonic claimed that its AI technology, called Aristotle, had solved an “Erdős problem” with the help of a collaborator: OpenAI’s latest technology, GPT-5.2 Pro.
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For many computer scientists and mathematicians, solving an Erdős problem demonstrated that AI had reached a point where it was capable of carrying out legitimate academic research. But some experts were quick to point out that the AI-generated solution wasn’t much different from previous work done by human mathematicians.
“To me, he looks like a very smart student who memorized everything for the test but doesn’t have a deep understanding of the concept,” said Terence Tao, a professor at UCLA, considered by many to be the greatest mathematician of his generation. “He has so much background knowledge that he can fake real understanding.”
The debate over what Harmonic’s system actually accomplished was a reminder of two recurring questions about the tech industry’s breakneck advance in AI development: Did the AI system really do something brilliant? Or did it just repeat something that had already been created by brilliant humans?
Answers to these questions can offer a better understanding of the ways AI can transform science and other fields. Whether or not AI is generating new ideas—and whether it could one day do a better job than human researchers—it is already becoming a powerful tool when placed in the hands of smart, experienced scientists.
These systems can analyze and store much more information than the human brain and can provide data that experts have never seen or have long forgotten.
Dr. Derya Unutmaz, a professor at Jackson Laboratory, a biomedical research institution, said the latest AI systems have gone so far as to suggest a hypothesis or experiment that he and his colleagues had not previously considered.
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“This is not a discovery. It’s a proposal. But it allows you to narrow down where you should focus,” said Unutmaz, whose research focuses on cancer and chronic diseases. “This allows you to do five experiments instead of 50. This has a profound and accelerating effect.”
The excitement around GPT-5’s mathematical abilities began in October, when Kevin Weil, vice president of science at OpenAI, said on social media that the startup’s technology had answered several of Erdős’ intriguing problems.
Created as a way to measure mathematical ingenuity, Erdős problems are conjectures or elaborate questions that test the limits of the field. The objective is to prove whether each one is right or wrong.
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Some problems are extremely difficult to solve, while others are easier. One of the most famous asks: if the integer n is greater than or equal to 2, can 4/n be written as the sum of three positive fractions? In other words, is there a solution to 4/n = 1/x + 1/y + 1/z?
This issue has not yet been resolved. But on social media, Weil boasted that GPT-5 had solved many others. “GPT-5 just found solutions to 10 (!) Erdős problems that previously had no solution and made progress on another 11,” Weil wrote. “They had all been open for decades.”
Mathematicians and AI researchers were quick to point out that the system had identified existing solutions, hidden in decades of academic articles and textbooks. The OpenAI executive deleted his post on social media. But even if the initial enthusiasm was exaggerated, the technology had proven its worth.
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“What he managed to do was surprising and useful,” said Thomas Bloom, a mathematician at the University of Manchester who maintains a website dedicated to Erdős’s problems. “One of the articles he found was written in German. I would never have found that on my own.”
So how has AI made such huge leaps since ChatGPT was introduced in late 2021? Today’s main AI systems are what scientists call neural networks, capable of identifying patterns in text, sounds and images and learning to generate this type of material on their own, including academic papers, computer code, voices and diagrams.
About 18 months ago, companies like OpenAI and Google began improving their systems using a technique called reinforcement learning. Through this process, an AI system can learn behaviors through extensive trial and error.
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The result is that these systems can now “reason” about problems in areas such as mathematics, science and computer programming. A system like GPT-5 doesn’t reason exactly like a human, but it can spend more time working on a problem. Sometimes this work goes on for hours.
(The New York Times has sued OpenAI and Microsoft, alleging copyright infringement of journalistic content related to AI systems. Both companies have denied the allegations.)
After Weil’s social media post, researchers continued to ask GPT-5 and other AI technologies for solutions to Erdős’ problems.
Kevin Barreto and Liam Price, two British mathematicians, used GPT-5 this month to solve a previously unsolvable problem. They then used Aristotle, Harmonic’s AI system, to verify that the solution was correct. Unlike GPT-5, Aristotle uses a specialized programming language to prove whether an answer is right or wrong.
The two mathematicians did have a small role. They pushed OpenAI’s system in a new direction when the test didn’t do exactly what they wanted. But, like other experts, they believe that AI has already demonstrated that it can do academic research.
“It’s not super high-level research, but the fact that AI is capable of doing research at any level is impressive,” Bloom said. If a graduate student showed him the same mathematical solution, he added, he would suggest that the student submit it to an academic journal for publication.
But while some experts applauded what the two AI systems had done, others were less enthusiastic. Tao said the solution was based on widely known methods.
“A consensus on what exactly the problem was asking was only reached in the last month or so, which may explain why it hadn’t been adequately addressed in the literature before,” he said.
Although he was impressed, Bloom added that he had not yet seen evidence that AI could generate ideas that humans cannot. “And I would be surprised if that happened anytime soon,” Bloom said.
Still, scientists say that AI has become a powerful and rapidly evolving research tool and that the question of whether or not it is generating ideas on its own is — for now — irrelevant.
When Unutmaz uses AI in his chronic disease research, he said he often feels like he’s talking to an experienced colleague.
But he recognizes that the machine cannot do the work without a human collaborator. An experienced researcher is still needed to repeatedly guide the system, explain what it should look for, and ultimately separate the interesting information from everything else the system produces.
“I’m still relevant, maybe even more relevant,” he said. “You have to have very deep expertise to appreciate what she’s doing.”
c.2026 The New York Times Company
