The paper introduces a new human‑AI collaboration paradigm for mathematical discovery, shifting from selecting individual problems to exploring broad research directions. It presents the Find, Attempt, and Recommend (FAR) pipeline, which automatically searches a literature corpus, filters candidate conjectures, and surfaces promising resolutions for expert review. In a combinatorics pilot, FAR processed over 5,000 papers, identified thousands of open conjectures, and ultimately highlighted 77 items that led to new discoveries.
By Zeyu Zheng, Shengtong Zhang, Jeremy Avigad, Prasad Tetali, Sean Welleck
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:2610.32575v1 Announce Type: new
Abstract: Large language models and agents have shown significant power in advanced physical research. In this paper, We introduce PHYRD, a living benchmark for...
By Qituan Zhang, Guo Chen, Linfeng Zhang, Wenlong Zhang
arXiv:2610.33690v1 Announce Type: new
Abstract: Many mathematical research agents focus on solving problems with fixed statements. However, conjecture research, especially in applied mathematics, may...
By Shu Miao, Feiming Wang, Wentao Long, Chenyi Li, Kun Yuan, Zaiwen Wen
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
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
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:2608. 16876v1 Announce Type: cross Abstract: We introduce Automatic Symbolic Regression (AutoSR), a fully automated system that instantiates Research-Space Symbolic Regression by searching persistent scientific investigations rather than isolated equations.
By Kejia Zhang, Youran Sun, Xinyu Ren, Chugang Yi, Haizhao Yang
arXiv:2607. 28684v1 Announce Type: new Abstract: Existing benchmarks for scientific equation discovery are largely composed of well-known equations available in the public domain, making it difficult to determine whether a model is discovering laws from data or merely recalling answers from its training corpus.
By Zhan'ao Yao, Liang Yin, Zhihao Gao, Boxuan Zhang, Xiaoyu Wu, Linjing Li, Rongyan Wang, Tingwei Chen, Youwei Wang, Xiaolin Zhao, Jiahui Shi, Jianjun Liu
arXiv:2606. 13566v1 Announce Type: new Abstract: Current discussions of AI in scientific discovery are often dominated by two visible capabilities: search over existing knowledge and execution through optimization, simulation, and automation.
By Guojun Liao
The paper introduces SCILAWS-BENCH, a benchmark for evaluating large language models (LLMs) on scientific law discovery. It contains 118 problems from 381 scientific papers, covering 291 candidate laws and about 8 million real data points across six disciplines. The benchmark offers two settings: SCILAWS-REAL, where models must propose laws from fixed real observations, and SCILAWS-PARALLEL, where models actively query synthetic worlds to recover hidden laws.
By Yiming Huang, Ziche Liu, Zhuohang Wu, Yiqian Wang, Junxia Cui, Xinkai Zou, Linjun Mao, Nan Huang, Naicheng Yu, Kaijie Zhu, Yue Ma, Kun Zhou, Letian Peng, Jingbo Shang
arXiv:2606. 09276v1 Announce Type: new Abstract: Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data.
By Paul Kahlmeyer, Henrik Voigt, Michael Habeck, Joachim Giesen