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
The paper introduces the AI Mathematician (AIM) framework, which leverages Large Reasoning Models (LRMs) to tackle frontier mathematical research. AIM addresses the complexity and procedural rigor of research problems through an exploration mechanism for longer solution paths and a pessimistic reasonable verification method for reliability. Early experiments show AIM can autonomously construct significant proof components and uncover non‑trivial insights across real‑world mathematical topics.
By Yuanhang Liu, Yanxing Huang, Yanqiao Wang, Peng Li, Yang Liu
arXiv:2607. 14178v1 Announce Type: new Abstract: Recent advances in Large Language Models have fueled autonomous AI agents capable of tackling complex scientific tasks, yet existing automated research systems remain predominantly focused on empirically driven domains with quantitative benchmarks, leaving theory-driven discovery, particularly in mathematically grounded disciplines requiring rigorous proofs and synthesis of domain knowledge, largely underexplored.
By Yutong He, Daibo Li, Guohong Li, Jiahe Geng, Zhengyang Huang, Can Ren, Zekun Zhang, Yifan Liu, Shuchen Zhu, Hengrui Zhang, Boao Kong, Ming Sun, Shu Li, Chenyi Li, Jiang Hu, Kun Yuan, Zaiwen Wen, Pingwen Zhang
The article compares how AI systems and human mathematicians approach 11 long-standing mathematical problems. It finds that AI reports focus more on solving the problem and linking ideas across fields, while human papers emphasize method explanation, assumptions, limitations, and future questions. Both approaches show similar levels of generality, but differ in their research profiles.
By Yang Ding
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
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.
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: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: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
ScholarCatalyst is a new benchmark that evaluates how well AI systems can retrieve research papers that inspire new work. The dataset was created by having 184 lead authors of 207 recent computer science papers annotate which earlier papers helped their projects, providing detailed rationales. The benchmark tests retrieval from the literature available at the start of a project, revealing that current agentic search and even advanced models like Claude Fable 5.1 perform only modestly better than simple embedding retrieval.
By Sohyeon Kim, Yoonho Lee, Bo Liu, Dayoon Ko, Rulin Shao, Seungone Kim, Graham Neubig, Pang Wei Koh, Aakanksha Chowdhery, Akari Asai, Omar Khattab, Yejin Choi, Gunhee Kim, Chelsea Finn
arXiv:2606. 10402v1 Announce Type: cross Abstract: Scientific discovery is often a collective process: researchers share partial results, inspect failed attempts, and build on each other's ideas over long time horizons.
By Federico Bianchi, Yongchan Kwon, Aneesh Pappu, James Zou
The paper introduces ScientistTwo, a fully autonomous multi‑agent framework that takes a scientific problem, establishes baselines, generates hypotheses, and coordinates specialized agents to conduct an end‑to‑end discovery cycle without human intervention. It rigorously tests and refines its methods through automated experiments, ablation studies, and a closed‑loop peer‑review engine. Benchmarking against top conferences (ICLR, ICML, NeurIPS) shows that ScientistTwo produces expert‑level, publishable papers and codebases that outperform human state‑of‑the‑art models and receive higher review ratings under automated AI review.
By Jaehyun Nam, Jinsung Yoon, Yanzhou Pan, Yubo Wang, Rui Meng, Parthasarathy Ranganathan, Tomas Pfister