FormalFlow is a system that coordinates AI proving agents under human supervision to tackle long‑horizon formalizations, using a shared blueprint for nested planning, proving, and review loops. The team used it to produce a machine‑checked Lean 4 proof of the quantum soundness of the classical low‑individual‑degree test, a core theorem underlying MIP* = RE, in 63 days. The resulting library contains 126,367 lines of Lean code, all generated by agents, and corrects side conditions while preserving the published error bound under corrected assumptions.
By Sirui Lu, Ruixuan Deng, Yanqiao Zhu, Zhengfeng Ji
AxQM is a new benchmark for formal proof synthesis in physics, comprising 1,019 Lean‑kernel‑checkable tasks drawn from the textbook *Quantum Computation and Quantum Information* by Nielsen and Chuang. The tasks are defined in a custom Lean library for finite‑dimensional quantum mechanics and are guaranteed solvable because they stem from a near‑complete formalization of the textbook’s formal content. Grading is deterministic, requiring proofs to compile, contain no sorrys, and introduce no new axioms.
By Weichen Winston Yin, Jacob M. Taylor, Dirk R. Englund, Frank H. L. Koppens
arXiv:2605. 22763v2 Announce Type: replace Abstract: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research.
By George Tsoukalas, Anton Kovsharov, Sergey Shirobokov, Anja Surina, Moritz Firsching, Gergely B\'erczi, Francisco J. R. Ruiz, Arun Suggala, Adam Zsolt Wagner, Eric Wieser, Lei Yu, Aja Huang, Mikl\'os Z. Horv\'ath, Andrew Ferraiuolo, Henryk Michalewski, Edward Lockhart, Codrut Grosu, Thomas Hubert, Matej Balog, Pushmeet Kohli, Swarat Chaudhuri
arXiv:2606. 06941v1 Announce Type: new Abstract: Large language models (LLMs) now solve a wide range of expert-level exams at or above human level, yet remain brittle on specialised, evidence-intensive domains such as law.
By Laura Wynter, Nirvik Sahoo, Paul Griffin
arXiv:2606. 03303v1 Announce Type: new Abstract: Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean.
By Po-Nien Kung, Linfeng Song, Dawsen Hwang, Jinsung Yoon, Chun-Liang Li, Simone Severini, Mirek Ol\v{s}\'ak, Edward Lockhart, Quoc V Le, Burak Gokturk, Thang Luong, Tomas Pfister, Nanyun Peng
arXiv:2505. 18492v5 Announce Type: replace Abstract: Mathematical competition problems fall into two broad types: theorem proving, which asks for a proof of a given statement, and answer construction, which requires constructing a property-satifying object with proofs.
By Jialiang Sun, Yuzhi Tang, Ao Li, Chris J. Maddison, Kuldeep S. Meel