arXiv:2606. 23821v1 Announce Type: cross Abstract: Accurate numerical eigenvalues are often difficult to certify, especially in singular or non-normal settings.
arXiv:2606. 17529v1 Announce Type: cross Abstract: Scientific machine-learning (SciML) surrogates approximate expensive simulations, but exact expected outputs for arbitrary inputs are unavailable (the oracle problem).
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.
arXiv:2606. 15096v1 Announce Type: new Abstract: The Riemann Hypothesis remains one of the central unsolved problems in mathematics.
arXiv:2607. 10474v1 Announce Type: cross Abstract: Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments.
arXiv:2607. 04505v1 Announce Type: new Abstract: We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction.
arXiv:2606. 21828v2 Announce Type: replace-cross Abstract: Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction.
Large language models (LLMs) have achieved remarkable performance on high-school and olympiad-style mathematics, yet their capabilities on advanced mathematics remain poorly understood. Existing benchmarks, however, fall short in both scope and evaluation granularity: they provide limited disciplinary coverage and often rely on final-answer correctness or coarse judgments, leaving the validity of the reasoning process inadequately assessed.
arXiv:2606. 08728v1 Announce Type: new Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers.
arXiv:2607. 01223v1 Announce Type: new Abstract: When should an AI system's answer be trusted?
arXiv:2601. 00791v2 Announce Type: replace-cross Abstract: Verifying whether a language model is genuinely reasoning or pattern-matching remains an open problem: learned verifiers are expensive, and output-based heuristics are brittle.
arXiv:2606. 24899v1 Announce Type: new Abstract: AI-assisted mathematics is often evaluated on solving predefined problems.
arXiv:2510. 16028v4 Announce Type: replace-cross Abstract: Neural networks increasingly run on hardware outside the user's control (cloud GPUs, inference marketplaces).