The largest math proof in human history is now computer-verified. Today, Axiom announces a complete Lean auto-formalization of the Classification of Finite Simple Groups, the "periodic table of symmetry." About 15,000 pages, built by over 100 mathematicians across generations.

Existence of Yang Mills? It’s just tying up a lose end for the hyper mathematically minded. I don’t think any physicist gives af. We have been doing precision calculations for decades. Of course it exists. But sure, would be nice to have a proof.

Behold: The US Defense Intelligence Agency has released a report on challenges to security in space, including an NEI image of China’s spaceplane from Maxar, taken in 2024.

More money, more time and flying less will not make spaceflight safer or make us more effective at achieving our objectives. We are done defending the status quo. We are not going to compromise NASA’s effectiveness or capability trying to appease every constituency and, in the process, satisfy no one. We are here for the mission, focused on executing @POTUS’ national space policy, achieving the objectives entrusted to us and delivering the kind of world-changing headlines worthy of America’s space program.

The physics collaboration will understand and explain a result that gives a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics. As a subproblem, this work also includes a proof of the existence of pure Yang–Mills theory, which is part of the Quantum Yang–Mills Theory Clay Mathematics Institute Millennium Prize problem. These proofs are all formally verified in Lean. Our models produced a natural language proof for Yang–Mills existence, and then subsequently produced a proof for QCD After the formalization completed, we reached out to David Gross. David will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work, and we will defer to them on the release of materials. Gross’s work on asymptotic freedom in Yang-Mills theories helped establish QCD as the theory of the strong interactions and earned him a share of the 2004 Nobel Prize in Physics. Jaffe formulated the Quantum Yang–Mills Theory Millenium Prize problem with Witten and also envisioned the idea of Millennium Prize problems and co-founded the Clay Mathematics Institute. Douglas has already been a steward of this problem over the last 20 years; Klebanov helped pioneer the application of gauge–string duality to confinement, an important property of QCD, and now directs the Simons Collaboration on Confinement and QCD Strings; and Nekrasov has done groundbreaking work on exact methods for generalizations of Yang–Mills theory.

The National Institutes of Health (NIH) has spent the past decade compiling information on hundreds of U.S.-based scientists it believes tried to illegally help their country of origin, most often China. But it’s never been clear what triggered NIH’s aggressive pursuit of these scientists, many of whom eventually lost their jobs or even went to jail, and why it was so much more extensive than efforts at other federal agencies. Mystery solved. Science has learned that Tam Dao, an academic psychologist–turned–FBI special agent for counterintelligence, laid the groundwork for NIH’s campaign. Dao remains an important player in the debate over research security. Now head of campus safety and research security at Rice University, he will be tackling a question that arguably should have been asked before NIH plunged ahead: How often do foreign governments try to steal research at U.S. universities? Read more: scim.ag/4staPfR