Abstract
<title>Abstract</title> <p>The intersection of large language models (LLMs) and mathematical discovery represents a rapidly evolving frontier in artificial intelligence research. This systematic literature review, conducted following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guidelines, examines the current state of research on using LLMs for generating new mathematical knowledge, including conjectures, theorems, lemmas, axioms, and counterexamples. From an initial pool of 63 records published through December 31, 2025, we identified 32 studies that met our inclusion criteria after rigorous screening. Our analysis reveals seven distinct technical paradigms: evolutionary search methods, reinforcement learning (RL) approaches, self-play and expert iteration, neuro-symbolic hybrid systems, in-context learning pipelines, specialized pretraining objectives, and equation discovery techniques. We amalgamate findings across formal verification systems (including Lean, Isabelle, PVS, and Metamath), along with datasets, evaluation metrics, and architectural choices. Our review identifies that evolutionary approaches combined with formal verification have achieved the most significant mathematical discoveries, including improvements to Strassen's matrix multiplication algorithm and solutions to open problems in extremal combinatorics. We provide a technical taxonomy to guide practitioners in designing novel architectures for mathematical discovery, highlighting both proven strategies and open challenges in this emerging field.</p>