Unexpected breakthrough: Chinese neurosurgeon proves mathematical hypothesis with GPT-5.6 that stumped experts for two decades

On August 14, 2026, the global scientific community was shaken by a sensational discovery at the intersection of medicine and artificial intelligence. Dr. Jin Shanmu, a neurosurgeon and researcher at Peking University Medical Center, successfully proved the Kruse hypothesis — one of the most complex problems in linear algebra, which mathematicians have been trying to solve since 2004. Notably, the latest OpenAI model, version GPT-5.6-Sol, running on the ChatGPT Work platform, played a key role in the solution.

From geology to medicine and mathematics: the path of a self-taught expert

Dr. Jin Shanmu’s biography is itself a rare example of interdisciplinary success. He does not have formal mathematical training. At university, he studied geology, then retrained in medicine, where his knowledge of mathematics was limited to basic courses for natural sciences. The rest of his knowledge base was accumulated independently, guided by personal interest.

Initially, Dr. Jin’s goal was not to solve a fundamental mathematical problem. He was trying to optimize a professional task related to brain ultrasound technology. In the process of data analysis, he encountered a complex area of matrix analysis that led him to the Kruse hypothesis.

The role of artificial intelligence in the proof

The key tool in the work was the GPT-5.6-Sol model. According to reports, the system worked continuously for 16 hours, helping the doctor structure his thoughts and verify calculations. The Kruse hypothesis states that the norm of any matrix function does not exceed twice the maximum value of this function in the numerical domain of the matrix. This problem has stumped experts around the world for two decades.

Dr. Jin’s success demonstrates how modern AI models can serve as a powerful catalyst for researchers who are not narrow specialists in a particular field but possess high motivation and the ability to self-learn.

Confirmation from the global community

Information about the breakthrough became public thanks to a chain of events initiated by prominent mathematicians. Professor Alex Townsend from Cornell University and Professor Anne Greenbaum from the University of Washington, who had been trying to solve this problem with the help of AI for more than a year, received a notification from the model on July 30. The AI led them to an article published on the internet three days earlier, where Jin Shanmu was listed as the lead author.

Mr. Townsend, Mr. Greenbaum, and the author of the hypothesis himself, Michel Kruse, reviewed the manuscript and confirmed the accuracy of the proof. Although the work has not yet undergone formal peer review in a peer-reviewed journal, the authority of these scientists gives the discovery maximum weight.

Context: AI as the new engine of science

This event is not an isolated fact but part of a global trend where AI is becoming the main tool for mathematical discoveries. Earlier this year, OpenAI announced an internal model that solved the 80-year-old unit distance problem on a plane posed by Paul Erdős. Progress in solving 10 other problems with the help of the Astra model was also reported.

In a competitive environment, the company Anthropic also claimed breakthroughs by its Claude model in the area related to the Riemann hypothesis. However, the case with Dr. Jin is unique in that the solution was found not by a professional mathematician, but by a practicing doctor using AI as a "co-pilot".

Contradictory data

During fact-checking, minor discrepancies were identified in details concerning chronology and technical nuances. Initial reports by some media outlets mentioned that the model worked for "several weeks," while in Dr. Jin's interview, he spoke of a continuous 16-hour session. Probably, this refers to two different stages: a 16-hour final proof session and a longer preliminary analysis.

There is also confusion in the names of the models. Some sources mention the "Astra" model as solving problems, while others mention "GPT-5.6-Sol". Given that Astra is positioned as an internal research model of OpenAI, and GPT-5.6-Sol as a version for the ChatGPT Work platform, it is possible that Dr. Jin used the public version, which is based on the same architectural principles as Astra.