A Chinese doctor has solved a mathematical problem that has puzzled leading mathematicians around the world for more than two decades, using the artificial intelligence model ChatGPT.
Jin Shanmu, a medical researcher at Peking University Medical College, was never a mathematician. He is a geology graduate who turned to medicine and then to researching brain imaging techniques. During his transition between these disciplines, he stumbled upon a complex mathematical problem known as "Crouzeix's conjecture," which was proposed by the French mathematician Michel Crozeix about twenty years ago. It relates to mathematical matrices—tables of numbers used in physics and computer science to solve equations and process data—but no mathematician has been able to provide conclusive proof of its validity throughout all these years.
Gene used OpenAI's advanced reasoning model as a tool for research and calculations, and despite his limited background in mathematics, artificial intelligence helped him overcome this obstacle. The result was a scientific paper in which he provided a conclusive proof of the problem, something even top mathematicians who were trying to solve it themselves hadn't anticipated.
At Cornell University, mathematician Alex Townsend and his colleagues were also using GPT models in an attempt to solve the same conjecture, but they were surprised late last month when ChatGPT told them that the problem had been solved three days earlier. After searching, it turned out that Gene had published a comprehensive paper providing the final solution. When Townsend reviewed the manuscript with his colleague Ann Greenbaum and with Kruzeks himself, everyone confirmed the validity of the proof, and overnight Gene went from being an unknown medical researcher to the focus of attention for mathematicians around the world.
This individual achievement not only demonstrated Jane's passion for knowledge and her ability to move between disciplines, but also revealed the growing capabilities of artificial intelligence in fields once considered the exclusive domain of trained human minds. Just a few months ago, OpenAI confirmed that one of its models had solved another mathematical problem posed by a Hungarian scientist in 1945. The company also announced that its new model had made significant progress on ten other complex mathematical problems. Similarly, its competitor, Anthropic, stated that its model, Claude, is currently attempting to solve the most famous unsolved mathematical problem in history: the Riemann Hypothesis.
Thus, artificial intelligence is no longer just a tool for writing letters or summarizing long memoirs, but has become a true partner in scientific discoveries, capable of enabling researchers from diverse backgrounds to achieve accomplishments that seemed unattainable years ago, opening the door to a new era of cooperation between humans and machines in uncovering the secrets of science that have remained pending for decades.
