The paper investigates how AI agents can discover and validate scientific formulas, focusing on the hydrotope—a geometric formula that unifies polynomial pieces of nonlinear surface-wave scattering. Through controlled experiments, the authors compare human–agent collaboration, single-prompt rediscovery, and various guided approaches, finding that only a PI$+$two-student workflow reliably reconstructs the full hydrotope and even uncovers a new analytic expression for the six-point amplitude $A_6$. The study highlights the challenges of combining exponentially many terms and the importance of coordinated analytic and numerical tasks for successful formula discovery.
arXiv:2607. 12122v1 Announce Type: new Abstract: We present an agentic approach to autonomous neural operator discovery based on an AI scientific community, which consists of a swarm of virtual laboratories that interact under a citation-based economy of influence.
arXiv:2609. 38369v1 Announce Type: new Abstract: We study generalized Blaschke curves as a controlled environment for AI-assisted mathematical rediscovery.
arXiv:2605.11280v2 Announce Type: replace-cross Abstract: Fast surrogate models for expensive simulations are now essential across the sciences, yet they typically operate as black boxes. We present...
We present an agentic approach to autonomous neural operator discovery based on an AI scientific community, which consists of a swarm of virtual laboratories that interact under a citation-based economy of influence. Highly-cited labs found new labs that follow their research direction and replace non-performing labs.
arXiv:2607. 14582v1 Announce Type: new Abstract: Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition.
The paper introduces a new human‑AI collaboration paradigm for mathematical discovery, shifting from selecting individual problems to exploring broad research directions. It presents the Find, Attempt, and Recommend (FAR) pipeline, which automatically searches a literature corpus, filters candidate conjectures, and surfaces promising resolutions for expert review. In a combinatorics pilot, FAR processed over 5,000 papers, identified thousands of open conjectures, and ultimately highlighted 77 items that led to new discoveries.
arXiv:2606. 01316v1 Announce Type: new Abstract: Scientific discovery demands intelligence, perseverance, and serendipity across vast search spaces.
arXiv:2607. 14178v1 Announce Type: new Abstract: Recent advances in Large Language Models have fueled autonomous AI agents capable of tackling complex scientific tasks, yet existing automated research systems remain predominantly focused on empirically driven domains with quantitative benchmarks, leaving theory-driven discovery, particularly in mathematically grounded disciplines requiring rigorous proofs and synthesis of domain knowledge, largely underexplored.
arXiv:2608. 05702v1 Announce Type: new Abstract: Scientific machine learning commonly validates models at the level of a subdomain, a benchmark split, or an explanation for one prediction.
arXiv:2608. 04872v1 Announce Type: cross Abstract: Symbolic regression aims to discover closed-form equations from data, but existing LLM-guided methods often rely on a unified proposal loop that compresses heterogeneous search failures into a scalar score and a single prompt.
arXiv:2607. 06820v1 Announce Type: new Abstract: Recent advances in AI for Mathematics have focused largely on autoformalization and theorem proving, leaving the role of Computer Algebra Systems (CAS) in agentic LLM workflows underexplored.
Symbolic regression aims to discover closed-form equations from data, but existing LLM-guided methods often rely on a unified proposal loop that compresses heterogeneous search failures into a scalar score and a single prompt. We propose A-SR, a self-evolving agentic framework that shifts the control unit from expression edits to role-conditioned evidence views.