{"paper":{"title":"One Example Shown, Many Concepts Known! Counterexample-Driven Conceptual Reasoning in Mathematical LLMs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Chao Qu, Hai-Tao Zheng, Haojing Huang, Jiayi Kuang, Philip S. Yu, Wenlian Lu, Xiaoyu Tan, Xinnian Liang, Yangning Li, Yinghui Li, Ying Shen, Yi Yu, Zhikun Xu","submitted_at":"2025-02-12T02:01:10Z","abstract_excerpt":"Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of \"proof by counterexamples\" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10454","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.10454/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}