The field of large language models (LLMs) is rapidly advancing, with a focus on improving mathematical reasoning and problem-solving capabilities. Recent developments have led to the creation of large-scale datasets, such as the Open Proof Corpus, which enable the evaluation and improvement of LLMs in mathematical proof generation. Additionally, hybrid approaches that combine rule-based systems with LLMs have shown promise in automatic generation of mathematical conjectures. LLMs are also being applied to various domains, including network optimization, UAV control, and theorem proving, with notable successes in generating human-like action sequences and solving stochastic modeling problems. However, challenges remain, such as addressing cultural gaps in mathematical problem presentation and improving the reliability of LLM-driven systems. Noteworthy papers include the introduction of LeanConjecturer, a pipeline for automatic generation of mathematical conjectures, and Bourbaki, a modular system for theorem proving that achieves state-of-the-art results on university-level problems. Furthermore, the development of frameworks such as RALLY and NL2FLOW demonstrates the potential for LLMs to be used in complex problem-solving tasks, such as role-adaptive navigation and parametric problem generation.
Advancements in Large Language Models for Mathematical Reasoning and Problem Solving
Sources
The Open Proof Corpus: A Large-Scale Study of LLM-Generated Mathematical Proofs
LeanConjecturer: Automatic Generation of Mathematical Conjectures for Theorem Proving
LMPVC and Policy Bank: Adaptive voice control for industrial robots with code generating LLMs and reusable Pythonic policies
Concept-Level AI for Telecom: Moving Beyond Large Language Models
Bootstrapping Human-Like Planning via LLMs
Performance of LLMs on Stochastic Modeling Operations Research Problems: From Theory to Practice
Large Language Models Don't Make Sense of Word Problems. A Scoping Review from a Mathematics Education Perspective
Mathematics Isn't Culture-Free: Probing Cultural Gaps via Entity and Scenario Perturbations
RALLY: Role-Adaptive LLM-Driven Yoked Navigation for Agentic UAV Swarms
Frontiers of Generative AI for Network Optimization: Theories, Limits, and Visions
Large Language Model-Driven Closed-Loop UAV Operation with Semantic Observations
Scaling LLM Planning: NL2FLOW for Parametric Problem Generation and Rigorous Evaluation
On the Convergence of Large Language Model Optimizer for Black-Box Network Management
Bourbaki: Self-Generated and Goal-Conditioned MDPs for Theorem Proving