A Beijing-based neurosurgeon and self-taught mathematician has cracked a decades-old mathematical puzzle previously unsolved since 2004 by leveraging the capabilities of OpenAI’s advanced AI model, GPT-5.6, marking a milestone in AI-assisted scientific discovery.
- Jin Shanmu, a neurosurgeon, solved Crouzeix’s conjecture with GPT-5.6.
- The conjecture had remained unsolved since 2004 in matrix analysis.
- The breakthrough highlights AI's accelerating impact in advanced math.
What happened
Jin Shanmu, a Beijing-based neurosurgeon and self-taught math enthusiast, used OpenAI’s latest AI model, GPT-5.6-Sol, to solve Crouzeix’s conjecture, a challenging mathematical problem first proposed in 2004. Using a 16-hour autonomous run on the ChatGPT Work platform, Jin was able to generate a proof for this decades-old puzzle, which has long frustrated experts in numerical linear algebra.
The conjecture suggests a relationship between the norm of a function applied to a matrix and the maximum value of the function on the matrix’s numerical range. Though abstract and complex, Jin arrived at the solution while conducting research related to brain ultrasounds. His work was subsequently validated by renowned mathematicians including Alex Townsend and Anne Greenbaum, and even by the conjecture’s original proposer, Michel Crouzeix, prior to formal peer review.
Why it matters
This breakthrough is significant as it demonstrates the increasing capability of AI, particularly models like GPT-5.6, to assist in solving hard mathematical problems autonomously. Jin’s success is all the more remarkable given his unconventional background; originally an undergraduate geology major, he transitioned to medicine and had limited formal mathematical training, relying mostly on self-study.
The development underscores the rising role of frontier AI systems in advancing scientific fields that have historically required deep specialist knowledge and intense intellectual effort. Breakthroughs like this could accelerate problem-solving in disciplines beyond mathematics, potentially revolutionizing research methodologies by combining human insight with AI computational prowess.
What to watch next
The growing application of large AI language models in mathematics will likely spark further breakthroughs in longstanding unsolved problems. OpenAI and competitors like Anthropic are actively deploying experimental models aimed at tackling famous challenges such as the Riemann hypothesis, indicating a new frontier for AI in foundational scientific research.
Observers should monitor the formal peer review process for Jin’s proof and subsequent independent validations. Additionally, developments in AI-driven research tools may scan across various domains including medicine, physics, and engineering, pushing forward innovation at a pace previously considered unattainable.