EULER is a multi‑agent system designed to facilitate the transfer of mathematical problems across different domains by constructing and evaluating ‘bridges’ that connect a source representation to a target representation. The system employs direct, adjacent‑domain, and distant‑domain search strategies, and uses six ordered stress tests to filter out invalid bridges before costly search. In experiments on 120 recent conjectures from combinatorics, EULER produced 10 proofs, 3 refutations, and 45 partial results, demonstrating that bridge‑specific stress tests and combined bridge‑material with target‑native operations significantly improve performance.
Automatically constructing well-specified and valuable mathematical conjectures remains a central challenge in AI-assisted mathematical discovery. Many existing open problems and conjectures are often too broad, underspecified, or difficult to connect to plausible proof or refutation strategies.
The paper introduces the AI Mathematician (AIM) framework, which leverages Large Reasoning Models (LRMs) to tackle frontier mathematical research. AIM addresses the complexity and procedural rigor of research problems through an exploration mechanism for longer solution paths and a pessimistic reasonable verification method for reliability. Early experiments show AIM can autonomously construct significant proof components and uncover non‑trivial insights across real‑world mathematical topics.
EPOCH is an evidence‑governed architecture for AI research agents that improves how candidate discoveries are evaluated and validated. By combining explicit task contracts, typed memory, active falsification, admission checks, and independent replay, EPOCH ensures that each candidate is judged against the strength and scope of its claim. The system achieves state‑of‑the‑art performance on several benchmarks, including AlgoTune, Math14, and AgentHPO, and demonstrates significant advances in executable constructions, algorithm optimization, counterexamples, and proof‑supported results across ten discovery problems.
The paper introduces Ansatz, a mathematical research agent that uses Continual Graph Memory to organize and reuse intermediate proof results across multiple problems. The system represents facts, plans, and counterexamples in a unified graph, enabling dependency-aware retrieval, evidence-sensitive curation, and scoped recall to guide long-horizon proof searches. Experiments show Ansatz solves all ten First Proof Second Batch problems, tackles the Jamison caterpillar conjecture, and makes progress on several Erdős problems without human help.
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.
Cogentic is a multi‑agent system designed to automate proof discovery for open research problems. It uses an iterative prove‑verify loop where an orchestrator assigns independent provers to different proof directions, verifies their outputs with specialized components, and records confirmed intermediate results in a persistent ledger for future rounds. Built on Gemini, Cogentic has produced novel results on five open problems in online learning, auction theory, and mechanism design, each verified by domain experts and detailed in companion papers.
arXiv:2605. 22763v2 Announce Type: replace Abstract: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research.
ULTRADISCOVERY is a benchmark that tests abductive exploration in an epistemically open, interconnected universe. It features five domains where agents must revise an initial theory and predict outcomes of unseen cross‑domain interventions, with a $2 imes 2$ design manipulating representation openness and evidence alignment. Experiments show that agents struggle to compose evidence into transferable representations, especially when the representation is open, and that even with aids exact predictions are rare without large budgets.
arXiv:2610.33690v1 Announce Type: new Abstract: Many mathematical research agents focus on solving problems with fixed statements. However, conjecture research, especially in applied mathematics, may...
AutoGraphForge is a computational pipeline designed to automate the discovery, refutation, formalization, and proving of graph-theoretic conjectures. It generates conjectures using a Graffiti3 generator, filters out known results with a novelty filter, tests candidates against a large dataset of graphs, and refines surviving conjectures through counterexample search. The pipeline then translates each conjecture into Lean 4, verifies proofs with neural provers, and integrates the results into a formal library.
arXiv:2608. 15979v1 Announce Type: new Abstract: Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules.
arXiv:2610.17090v1 Announce Type: cross Abstract: On 6 October 2026 OpenAI published an initial 722 AI-written mathematical manuscripts, organized into 372 problem families, in the public repository...