On October 26, 2026, OpenAI made an extraordinary announcement: its artificial intelligence systems had reportedly produced a mathematical proof of the existence of four-dimensional quantum Yang–Mills theory.
Yang–Mills theory is one of the foundations of modern particle physics. It provides the mathematical framework underlying the strong and weak nuclear interactions. Yet despite its remarkable physical success, its rigorous mathematical construction remains one of the great outstanding problems of theoretical physics.
In 2000, the Clay Mathematics Institute included Yang–Mills theory among its seven Millennium Prize problems, each carrying a one-million-dollar prize.
The challenge has two parts: proving that the interacting quantum theory exists mathematically, and proving that its physical spectrum possesses a strictly positive mass gap.
OpenAI claims to have solved the first part, not the second.
An independent committee of distinguished physicists, chaired by Nobel laureate David Gross, is examining the proposed proof. Its mathematical validity and physical significance remain under assessment.
In my new video, The Yang–Mills Millennium Problem: Quantum Field Theory and the Age of Industrial-Scale AI Physics, I explain the history and physics of Yang–Mills theory, the mathematical difficulties behind its rigorous construction, and the pioneering work of Tadeusz Balaban on constructive renormalization.
We then examine what OpenAI has actually announced, what remains to be verified, and why this episode may signal a new era of industrial-scale AI-assisted mathematical and theoretical physics.
The presentation is intended for physics students, researchers, and anyone interested in the foundations of modern physics.
Download the essay:
https://drive.google.com/file/d/1XC5_3KVcUwu6TEikTv9z_tWM-g4g_P_k/view?usp=sharing
Full English video (Badis Ydri | QUANTUM):
https://www.youtube.com/watch?v=BfzTZT4LRuQ
Short Arabic introduction (Badis Ydri | ARCHIVE):
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