EULER: Exploring Underused Links with Evidence-Checked Return for Multi-Agent Mathematical Discovery

Researchers introduced EULER, a multi-agent system for mathematical discovery that searches for cross-domain bridges, and reported that it produced 10 proofs, 3 refutations, and 45 scoped partial results across 120 recent conjectures from combinatorics. The system's bridge-specific stress tests reduced incorrect conclusions from 9 to 3, and combining bridge material with target-native operations yielded a positive interaction of +4.2 resolved tasks. The findings suggest that executable operation gain and valid return, rather than domain distance, predict success in mathematical discovery.

arXiv:2609.00032v1 Announce Type: new Abstract: Mathematical communities work with different objects, invariants, and tools, so transferring a problem across them is expensive and often skipped. We present EULER, a multi-agent system that takes such a transfer--a bridge--as its unit of search. Around a fixed conjecture, EULER runs direct, adjacent-domain, and distant-domain routes in competition; a bridge keeps its budget only if it supplies an operation the source representation cannot execute and its target-side evidence returns to the original statement along a checked implication. Six ordered stress tests reject invalid bridges before expensive search begins. We evaluate EULER on 120 recent conjectures. The conjectures were frozen before search and screened for contamination, and are drawn from public papers by authors who had recently published in the Journal of Combinatorial Theory, Series A, a leading journal in combinatorics. EULER produced 10 proofs and 3 refutations, plus 45 scoped partial results. Two mechanisms held up under ablation: bridge-specific stress tests cut incorrect conclusions from 9 to 3, and bridge material combined with a target-native operation yielded a positive interaction of +4.2 resolved tasks that neither factor produced alone. Domain distance did not reliably predict success; executable operation gain and valid return did.