arXiv Machine Learning
Sep 11

Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification

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 AI
Sep 28

PhysElite: How Far Are LLMs from Solving Olympiad-Level Physics Problems?

PhysElite is a new bilingual multimodal benchmark designed to evaluate large language models on Olympiad-level physics problems. It contains 11,586 problems, each paired with visual diagrams, step-by-step bilingual Chinese‑English solution derivations, and the final answer. Benchmarking 18 models revealed that even the best reaches only 33.7% accuracy, and a step‑level analysis highlights where models falter in reasoning.

By Ruoran Xu, Wending Gao, Liyunfeng Chen, Aixin Shi, Haoyu Cheng, Zixiang Fang, Yiqiang Zou, Qiufeng Wang
arXiv Machine Learning
Oct 15

Beyond Equation Search: Conjecture-Guided Discovery with SCOPE and ClosureBench

The paper introduces SCOPE, a framework that enables multiple scientist agents to pursue conjecture-driven research trajectories by modeling equations, formulating questions, and conducting active experiments, then sharing evidence to refine their conjectures. It also presents ClosureBench, an interactive benchmark of 60 closure-discovery tasks across five scientific domains, designed to evaluate equation discovery beyond accuracy by measuring evidence faithfulness, mechanism insight, and experimental effectiveness. Experiments show that SCOPE outperforms diverse baselines on both ClosureBench and a real-world scientific discovery case, yielding more accurate, reliable, and effective scientific discoveries.

By Yuxiao Hu, Qian Li, Ding Wang, Siheng Chen, Linfeng Zhang, Jinyue Yan, Yuntian Chen