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:2606. 24899v1 Announce Type: new Abstract: AI-assisted mathematics is often evaluated on solving predefined problems.
By Yanqiao Wang, Jin-Peng Liu, Peng Li, Yang Liu
arXiv:2606. 29687v1 Announce Type: cross Abstract: We report a machine-verified resolution of a problem open for over a decade in quantum optimization: the Farhi, Goldstone and Gutmann (FGG) conjecture that depth-$p$ Quantum Approximate Optimization Algorithm (QAOA) on the ring of disagrees attains approximation ratio $(2p+1)/(2p+2)$ exactly.
By Uri Kol, Maor Ben-Shahar, Kfir Sulimany, Dirk Englund
arXiv:2607. 14582v1 Announce Type: new Abstract: Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition.
By Junjie Zhang, Jiayu Liu, Wenbin Liu, Zhenya Huang, Doudou Wang, Yan Jiang, Leiye Xu, Tao Xiong, Wen Huang, Qi Liu, Guoping Hu, Enhong Chen, Mengping Zhang, Xiangdong Ye
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. 08728v1 Announce Type: new Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers.
By Syed Rifat Raiyan, Mohsinul Kabir, Hasan Mahmud, Md Kamrul Hasan
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
arXiv:2604. 03789v2 Announce Type: replace-cross Abstract: Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems.
By Haocheng Ju, Guoxiong Gao, Jiedong Jiang, Bin Wu, Zeming Sun, Shurui Liu, Leheng Chen, Yutong Wang, Yuefeng Wang, Zichen Wang, Wanyi He, Peihao Wu, Liang Xiao, Ruochuan Liu, Bryan Dai, Bin Dong
arXiv:2608.28639v1 Announce Type: new
Abstract: Formal theorem proving with large language models remains challenging due to the difficulty of navigating large proof search spaces efficiently. Existi...
By Bodla Krishna Vamshi, Haizhao Yang
The paper introduces HorizonMath, a benchmark of 113 largely unsolved mathematical problems across eight domains, paired with an open-source framework for automated verification. It focuses on the generator‑verifier gap, targeting problems that are hard to discover but easy to verify computationally, thereby avoiding costly formal proof verification or manual review. Using this framework, the authors found six novel solutions—three each from GPT‑5.4 Pro and GPT‑5.6 Sol—demonstrating that current models can contribute to mathematical research, while most state‑of‑the‑art models score below 10%.
By Erik Y. Wang, Sumeet R. Motwani, James V. Roggeveen, Eliot Hodges, Dulhan Jayalath, Charles London, Kalyan Ramakrishnan, Jakob Foerster, Cheng Zhang, Flaviu Cipcigan, Philip Torr, Alessandro Abate
QEncodeBench evaluates whether large language models can translate classical constraint problems into verified quantum phase oracles. The benchmark measures the correctness of generated circuits using an adversarial self‑validated verifier that checks full solution‑set equivalence while enforcing resource limits. Results show that models lacking a reasoning mode perform poorly, whereas enabling native reasoning improves accuracy tenfold; semantic errors dominate, and neuro‑symbolic pipelines close most gaps by delegating critical composition to deterministic procedures.
By Xujun Che, Hanhan Wu, Yuchen Yuan, Chenyang Yu
arXiv:2604. 19341v2 Announce Type: replace-cross Abstract: Scientific discovery often requires many cycles of proposing, testing, and refining candidate solutions.
By Haotian Ye, Haowei Lin, Jingyi Tang, Yizhen Luo, Rahul Thapa, Caiyin Yang, Chang Su, Rui Yang, Ruihua Liu, Rundao Li, Zeyu Li, Pengwei Sun, Chong Gao, Dachao Ding, Guangrong He, Miaolei Zhang, Lina Sun, Wenyang Wang, Yuchen Zhong, Zhuohao Shen, Puheng Li, Pan Lu, Bianxiao Cui, Di He, Jianzhu Ma, Junfeng Li, Hexi Baoyin, Yejin Choi, Stefano Ermon, Xiaowen Chu, Tongyang Li, Yuzhi Xu, James Zou