文章背景与核心概要
在现代数学研究中，不同数学分支依赖于各自独特的对象、不变量和工具，这使得跨领域的数学问题迁移成本高昂且常常被忽视。为了突破这一瓶颈，本文推出了 EULER（一种专为多智能体数学发现设计的系统），它将跨领域的数学问题迁移（称为“桥梁”）作为搜索的基本单位。
围绕一个固定的猜想，EULER 能够同时测试直接路径、邻近领域路径以及远距离领域路径。只有当“桥梁”引入了源表示无法执行的新操作，并能沿着经过验证的蕴含关系成功将目标侧的证据回传至原始命题时，它才会保留其计算预算。此外，为了防止计算资源的浪费，无效的桥梁在进行深度搜索之前会通过六项有序的压力测试被自动过滤掉。
EULER: Exploring Underused Links with Evidence-Checked Return for Multi-Agent Mathematical Discovery
Authors: Ren Zhenzhuo
Subjects: Artificial Intelligence (cs.AI); Multiagent Systems (cs.MA)
arXiv Identifier: arXiv:2609.00032 [cs.AI]
Submitted: 28 August 2026
Comments: 55 pages, 10 figures, 29 tables; includes a 13-page companion candidate-proof manuscript as Appendix P.
Authors: Ren Zhenzhuo
Subjects: Artificial Intelligence (cs.AI); Multiagent Systems (cs.MA)
arXiv Identifier:arXiv:2609.00032 [cs.AI]
Submitted: 28 August 2026
Comments: 55 pages, 10 figures, 29 tables; includes a 13-page companion candidate-proof manuscript as Appendix P.
📌 Summary
Mathematical communities rely on diverse objects, invariants, and tools, making the cross-domain transfer of problems expensive and often neglected. This paper introduces EULER, a multi-agent system designed to treat cross-domain problem transfer—referred to as a "bridge"—as its primary unit of search.
Operating around a fixed conjecture, EULER tests direct, adjacent-domain, and distant-domain routes concurrently. A bridge retains its computational budget only if it introduces an operation the source representation cannot execute and successfully returns target-side evidence back to the original statement along a verified implication. To prevent wasted resources, invalid bridges are filtered out via six ordered stress tests prior to deep searching.
📌 Summary
Mathematical communities rely on diverse objects, invariants, and tools, making the cross-domain transfer of problems expensive and often neglected. This paper introduces EULER, a multi-agent system designed to treat cross-domain problem transfer—referred to as a "bridge"—as its primary unit of search.
Operating around a fixed conjecture, EULER tests direct, adjacent-domain, and distant-domain routes concurrently. A bridge retains its computational budget only if it introduces an operation the source representation cannot execute and successfully returns target-side evidence back to the original statement along a verified implication. To prevent wasted resources, invalid bridges are filtered out via six ordered stress tests prior to deep searching.
📊 Evaluation & Results
EULER was evaluated on 120 recent conjectures frozen before search, screened for contamination, and sourced from public papers published by authors in the Journal of Combinatorial Theory, Series A.
- Outcomes: Produced 10 proofs, 3 refutations, and 45 scoped partial results.
- Ablation Studies:
- Bridge-specific stress tests successfully reduced incorrect conclusions from 9 down to 3.
- Combining bridge material with a target-native operation yielded a positive interaction of +4.2 resolved tasks compared to either factor in isolation.
- Domain distance was found not to be a reliable predictor of success; instead, executable operation gain and valid evidence return served as the true drivers of performance.
📊 Evaluation & Results
EULER was evaluated on 120 recent conjectures frozen before search, screened for contamination, and sourced from public papers published by authors in the Journal of Combinatorial Theory, Series A.
- Outcomes: Produced 10 proofs, 3 refutations, and 45 scoped partial results.
- Ablation Studies:
- Bridge-specific stress tests successfully reduced incorrect conclusions from 9 down to 3.
- Combining bridge material with a target-native operation yielded a positive interaction of +4.2 resolved tasks compared to either factor in isolation.
- Domain distance was found not to be a reliable predictor of success; instead, executable operation gain and valid evidence return served as the true drivers of performance.
🔗 Full-Text & Resources
🔗 Full-Text & Resources