Article by Cade Metz: “For decades, elite mathematicians have struggled to solve a collection of thorny problems posed by a 20th-century academic named Paul Erdos.
This month, an artificial intelligence start-up called Harmonic jumped into the mix. Harmonic said its A.I. technology, Aristotle, had solved an “Erdos problem” with help from a collaborator: OpenAI’s latest technology, GPT-5.2 Pro.
For many computer scientists and mathematicians, solving an Erdos problem showed that artificial intelligence had reached a point where it was capable of doing legitimate academic research. But some experts were quick to point out that the solution generated by A.I. was not very different from earlier work done by human mathematicians.
“It feels to me like a really clever student who has memorized everything for the test but doesn’t have a deep understanding of the concept,” said Terence Tao, a professor at the University of California, Los Angeles, who is regarded by many as the finest mathematician of his generation. “It has so much background knowledge that it can fake actual understanding.”
The debate over what Harmonic’s system accomplished was a reminder of two consistent questions about the head-spinning progress of the tech industry’s A.I. development: Did the A.I. system truly do something brilliant? Or did it merely repeat something that had already been created by brilliant humans?
The answers to those questions could provide a better understanding of the ways A.I. could transform science and other fields. Whether A.I. is generating new ideas or not — and whether it may one day do better work than human researchers — it is already becoming a powerful tool when placed in the hands of smart and experienced scientists.
These systems can analyze and store far more information than the human brain, and can deliver information that experts have never seen or have long forgotten.
Dr. Derya Unutmaz, a professor at the Jackson Laboratory, a biomedical research institution, said the latest A.I. systems had reached the point where they would suggest a hypothesis or an experiment that he and his colleagues had not previously considered.
“That is not a discovery. It is a proposal. But it lets you narrow down where you should focus,” said Dr. Unutmaz, whose research focuses on cancer and chronic diseases. “It allows you to do five experiments rather than 50. That has a profound, accelerating effect.”
The excitement around GPT-5’s math skills began in October when Kevin Weil, vice president of science at OpenAI, said on social media that the start-up’s technology had answered several of the mind-bending Erdos problems.
Designed as a way of measuring mathematical ingenuity, the Erdos problems are elaborate conjectures or questions that test the limits of the field. The aim is to prove whether each is right or wrong.
Some problems are enormously difficult to solve, while others are easier. One of the more famous problems 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?
That problem is still unsolved. But on social media, Mr. Weil boasted that GPT-5 had cracked many others. “GPT-5 just found solutions to 10 (!) previously unsolved Erdos problems, and made progress on 11 others,” Mr. Weil wrote. “These have all been open for decades.”
Mathematicians and A.I. researchers quickly pointed out that the system had identified existing solutions buried in decades of research papers and textbooks. The OpenAI executive deleted his social media post. But even if the initial excitement was overstated, the technology had proved its worth…(More)”.
