The paper introduces a method for evaluating the intrinsic interestingness of mathematical theorems by comparing the length of their proofs to the length of their statements. It trains a 27B language model to predict proof difficulty, enabling the generation and selection of more interesting theorems while significantly reducing overlap with existing Mathlib. The approach allows iterative expansion of a self‑building, machine‑verified mathematical library guided by quantifiable metrics.
By Niket Patel, Ahmad Rammal, Amaury Hayat, Remi Munos, Julia Kempe
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
arXiv:2606. 06526v1 Announce Type: new Abstract: Large language models have made substantial progress on mathematical reasoning, but existing benchmarks typically evaluate well-specified problems with final answers, step-by-step solutions, or complete proofs.
By Sherin Muckatira, Jesse Geneson, Slava Gerovitch, Pavel Etingof, Mikhail Gronas, Anna Rumshisky
arXiv:2610.17090v1 Announce Type: cross
Abstract: On 6 October 2026 OpenAI published an initial 722 AI-written mathematical manuscripts, organized into 372 problem families, in the public repository...
By Ying Xie
Automatically constructing well-specified and valuable mathematical conjectures remains a central challenge in AI-assisted mathematical discovery. Many existing open problems and conjectures are often too broad, underspecified, or difficult to connect to plausible proof or refutation strategies.
The paper introduces GAP, a methodology that automatically generates mathematically equivalent variants of existing math problems using surface renames and kernel rewrites. Applying GAP to all 1,051 William Lowell Putnam Competition problems creates PutnamGAP, a 6,306-item dataset with 5,255 unseen variants. Evaluation of 18 commercial and open-source LLMs shows accuracy drops across all models, especially under kernel rewrites, indicating a persistent weakness in transferring proof plans to new mathematical settings.
By Yuren Hao, Xiang Wan, ChengXiang Zhai
We construct OEIS Open, a benchmark based on 492 open mathematical conjectures from the OEIS, formalized in Lean by Tsoukalas et al. Whereas these conjectures had previously been attempted only with a bespoke agent, our open-source evaluation code runs any generic language model (LM) against them, and is secure against LM cheating attempts.
arXiv:2606. 10479v1 Announce Type: new Abstract: Combinatorics is central to Olympiad-level mathematical problem solving, requiring deep discrete reasoning, creative constructions, and rigorous structural insight.
By Shunkai Zhang, Haoran Zhang, Yun Luo, Qianjia Cheng, Haodi Lei, Yizhuo Li, Runzhe Zhan, Zhilin Wang, Bangjie Xu, Yucheng Su, Xinmiao Han, Xiaoye Qu, Dongrui Liu, Zhouchen Lin, Yu Qiao, Ning Ding, Yafu Li, Yu Cheng
arXiv:2608. 15979v1 Announce Type: new Abstract: Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules.
By Eric Xie, Wenqian Ye, Aidong Zhang
arXiv:2607. 28632v1 Announce Type: new Abstract: Major mathematical conjectures still depend heavily on expert intuition, so a unified method for the systematic generation and validation of conjectures with substantial mathematical potential remains unavailable.
By Alizer Wong, Zixin Zeng, Yi Tan, Wenyuan Li, Xuhang Chen, Xingru Lai, Yang Shi, Liangsi Lu, Yanhui Chen
MathAdv is a diagnostic benchmark for formal theorem proving that covers 13 undergraduate- and graduate-level mathematics domains. It includes Lean 4 proofs and up to three auxiliary tasks—multiple-choice questions, fill-in-the-blank problems, and expert-crafted transformations—to probe knowledge, informal reasoning, and robustness to problem presentation. Evaluation of current theorem provers shows formalization is a major bottleneck, performance varies by domain, natural-language guidance can help or hinder models, and equivalent reformulations reveal significant robustness gaps.
By Jiaxin Yuan, Connor Martinez Lockhart, Xiaoyu Liu, Jiaqi Wang, Chenghao Deng, Xiayimei Han, Vlasios Mastrantonis, Dmitrii Gudin, Shaopeng Zhu, Abdirisak Abdullahi Mohamed, Bilal Hamdi Aytekin, Jiewen Lang, Zezheng Song, Furong Huang
arXiv:2608. 11941v1 Announce Type: new Abstract: We construct OEIS Open, a benchmark based on 492 open mathematical conjectures from the OEIS, formalized in Lean by Tsoukalas et al.
By Tom Adamczewski