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
arXiv:2512.09443v3 Announce Type: replace-cross
Abstract: We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propos...
By Chenyi Li, Zhijian Lai, Dong An, Jiang Hu, Zaiwen Wen
arXiv:2607. 09632v1 Announce Type: cross Abstract: Quantum information theory (QIT) characterizes the capabilities and fundamental limits of quantum information processing, underpinning quantum communication, computation, and error correction.
By Chengkai Zhu, Ziao Tang, Guocheng Zhen, Yimeng Cao, Yusheng Zhao, Ranyiliu Chen, Xuanqiang Zhao, Lei Zhang, Xin Wang
arXiv:2606. 06468v1 Announce Type: new Abstract: We introduce Goedel-Architect, an agentic framework for formal theorem proving in Lean 4 centered on blueprint generation and refinement.
By Jui-Hui Chung, Ziyang Cai, Zihao Li, Qishuo Yin, Rohit Agarwal, Simon Park, Rodrigo Porto, Narutatsu Ri, Ziran Yang, Shange Tang, Xingyu Dang, Hongzhou Lin, Mengdi Wang, Danqi Chen, Chi Jin, Liam H Fowl, Sanjeev Arora
AdvancedMathBench is a new benchmark suite that evaluates large language models on advanced mathematical proof generation and verification. It includes ProverBench, with 245 problems from undergraduate to doctoral qualifying‑exam levels, and VerifierBench, which tests models’ ability to judge proof validity using 888 expert‑annotated trajectories. The suite features an automatic verification pipeline trained on expert data, and results show that even state‑of‑the‑art models perform poorly, highlighting a gap between generation and verification skills.
By Lingkai Kong, Zijian Wu, Yuzhe Gu, Haiteng Zhao, Zhouqi Hua, Wenyong Huang, Shuang Sun, Zhicheng Xiong, Xiaotian Zhang, Shuya Zhao, Yan Wang, Disheng Xu, Wenwei Zhang, Kai Chen
QuantumNovelty is an open‑source, skill‑orchestrating language agent that both creates quantum‑computing artifacts—such as papers, ansatz candidates, and patent drafts—and evaluates them through simulated referee and patent‑examiner panels. Its core innovation is an audit‑and‑falsify layer of deterministic gates (Pareto domination, numerical recomputation, Wilson intervals, and cross‑vendor consensus) that restricts claims to those that survive rigorous checks, with every model call logged for transparency. In initial tests on a planted adversarial corpus and a small real‑world deployment, the system successfully flagged all overclaims without false positives and produced panels that were more conservative than typical public acceptance rates.
By Shlomo Kashani
Large language models (LLMs) have achieved remarkable performance on high-school and olympiad-style mathematics, yet their capabilities on advanced mathematics remain poorly understood. Existing benchmarks, however, fall short in both scope and evaluation granularity: they provide limited disciplinary coverage and often rely on final-answer correctness or coarse judgments, leaving the validity of the reasoning process inadequately assessed.