EULER: A Multi-Agent System for Cross-Domain Mathematical Conjecture Solving via Bridged Transfer (arXiv 2509.00009)

Forum topic · 小凯 · 2026-09-03

Summary

EULER is a multi-agent AI system for mathematics that treats cross-community problem transfer—a bridge—as its unit of search, addressing the high cost of moving problems between mathematical communities that use different objects, invariants, and tools. Around a fixed conjecture, EULER runs direct, adjacent-domain, and distant-domain routes in competition; a bridge retains 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. Evaluated on 120 recent conjectures frozen before search and screened for contamination, drawn from authors publishing in the Journal of Combinatorial Theory, Series A, EULER produced 10 proofs, 3 refutations, and 45 scoped partial results. Ablations show bridge-specific stress tests reduced false conclusions from 9 to 3, and combining bridge material with target-native operations yielded a +4.2 positive interaction on solved tasks. Domain distance did not reliably predict success; executable operation gain and valid return did.

Overview

Field: Machine Learning
Authors: Ren Zhenzhuo
Published: 2026-09-03
arXiv: 2509.00009

Abstract (translated from Chinese)

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. These conjectures were frozen before search and screened for contamination, and are drawn from recent papers by authors publishing in the *Journal of Combinatorial Theory, Series A* (the leading journal in combinatorics). EULER produced 10 proofs and 3 refutations, along with 45 scoped partial results.

Two mechanisms survived ablation: bridge-specific stress tests reduced false conclusions from 9 to 3, and combining bridge material with target-native operations produced a +4.2 positive interaction on solved tasks—an effect neither factor achieved alone. Domain distance does not reliably predict success; executable operation gain and valid return do.

Original Abstract (English)

> 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 recen...

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