Euclid-Omni is a unified neuro‑symbolic framework that integrates a formal geometry system with Large Language Models and Vision‑Language Models to solve both calculation and proving problems in Euclidean geometry up to Olympiad level. Its core component, Euclidea, automatically generates deductive reasoning steps and algebraic computations, while a data‑generation pipeline creates synthetic symbolic problems, diagrams, and natural‑language translations for training. Experiments show that VLMs trained on this synthetic data outperform on calculation tasks, and LLMs paired with Euclidea match state‑of‑the‑art proving systems using far less compute and data.
By Zhaoyu Li, Hangrui Bi, Youyuan Zhang, Wenjie Ma, Zenan Li, Zhaolei Zhang, Xujie Si, Kaiyu Yang
arXiv:2608. 14221v1 Announce Type: new Abstract: Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4.
By Lushi Pu, Weiming Zhang, Xinheng Xie, Zixuan Fu, Bingxiang He, Hengyu Zhao, Hongya Lyu, Xin Li, Jie Zhou, Yudong Wang
The paper introduces TopoAlign, a framework that repurposes code repositories to train Math LLMs by decomposing code into docstrings, main functions, and dependency functions and reassembling them into structures that mirror formal mathematical statements. Using this approach, the authors train three state‑of‑the‑art models—DeepSeek‑Math, Qwen‑3, and Herald—and evaluate them on MiniF2F, Putnam, and ProofNet benchmarks. TopoAlign yields significant performance gains, notably a 17.77% improvement on BEq@10 and a 68.82% boost on typecheck@10 for DeepSeek‑Math, while also providing modest gains for Herald.
By Yupei Li, Philipp Borchert, Gerasimos Lampouras
NL2AGBench is a benchmark that evaluates how well large language models can translate English geometry problems into the formal language required by AlphaGeometry’s theorem‑proving engine. The study tests ten state‑of‑the‑art LLMs, comparing executable translation accuracy, syntactic correctness, and error types, and finds a large gap between closed‑source and open‑source models. The authors also propose an error taxonomy and test mitigation strategies such as few‑shot prompting, fine‑tuning, and human‑guided hinting, which improve performance across model families.
By Samuel Xiao, Judy Song, Rory Hu, Ziliang Zong
arXiv:2606. 13782v1 Announce Type: new Abstract: Large Language Models (LLMs) have made notable progress in automated theorem proving, yet existing formal benchmarks remain limited in both mathematical coverage and difficulty.
By Lushi Pu, Weiming Zhang, Xinheng Xie, Zixuan Fu, Bingxiang He, Hongya Lyu, Xin Li, Jie Zhou, Yudong Wang
arXiv:2512. 10187v3 Announce Type: replace Abstract: LLMs excel at reasoning, but validating their steps remains challenging.
By Mantas Baksys, Stefan Zetzsche, Olivier Bouissou, Sean B. Holden
arXiv:2606. 31134v1 Announce Type: new Abstract: While Large Language Models (LLMs) have demonstrated exceptional capabilities in mathematical reasoning, they frequently produce subtle errors that evade human detection.
By Arshia Soltani Moakhar, Iman Gholami, Max Springer, Mahdi JafariRaviz, MohammadTaghi Hajiaghayi
arXiv:2606. 12594v1 Announce Type: new Abstract: Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive.
By Joshua Ong Jun Leang, Zheng Zhao, Mihaela C\u{a}t\u{a}lina Stoian, Qiyuan Xu, Haonan Li, Wenda Li, Shay B. Cohen, Eleonora Giunchiglia
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
arXiv:2510. 04520v2 Announce Type: replace Abstract: Accurate auto-formalization of theorem statements is essential for advancing automated discovery and verification of research-level mathematics, yet remains a major bottleneck for LLMs due to hallucinations, semantic mismatches, and their inability to synthesize new definitions.
By Hanyu Wang, Ruohan Xie, Yutong Wang, Guoxiong Gao, Xintao Yu, Bin Dong
arXiv:2508.02208v3 Announce Type: replace-cross
Abstract: Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short...
By Yebo Peng, Yaoming Li, Zixiang Liu, Zhizhuo Yang, Xinye Xu, Bowen Ye, Weijun Yuan, Zihan Wang, Tong Yang
arXiv:2602.18307v2 Announce Type: replace-cross
Abstract: Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-b...
By Yutong Xin, Qiaochu Chen, Greg Durrett, I\c{s}il Dillig