On October 26, 2026 (local time), OpenAI unveiled three groundbreaking achievements spanning mathematics, computer science, and physics. In the realm of mathematics, AI successfully proved the local smoothness conjecture, a universal principle applicable across all dimensions, thereby resolving both the Kakeya conjecture and the Stein restriction conjecture. In computer science, it debunked the long-standing and widely embraced Exponential Time Hypothesis (ETH), hinting at the possibility of discovering even faster algorithms in the near future. In the field of physics, AI furnished a rigorous mathematical proof confirming the existence of quantum chromodynamics and Yang-Mills theory, thus tackling one of the Millennium Prize Problems. The pertinent findings have undergone Lean formal verification and are now accessible to the public on GitHub. However, they still await further independent validation from the academic community.
