NSF Award
2434704
The objective of this project is to enhance the functionality of interactive theorem provers (ITPs) in mathematical reasoning by integrating advanced artificial intelligence (AI) technologies with formal methods. This endeavor, named MathScy, aims to assist in conjecture formulation, proof construction, and counterexample finding. The current limitations of ITPs include scalability, adaptability, and the depth of reasoning required to tackle complex mathematical problems. Addressing these issues, MathScy promotes the progress of science and contributes to the national interest by advancing mathematical research, supporting education, and fostering diversity. The project will utilize the latest advancements in Large Language Models (LLMs) and will be intuitive and accessible to mathematicians, guided by principles of Human-Centered AI and Explainable AI. This approach ensures that the AI tools developed are user-friendly and can provide understandable explanations of their reasoning steps, thereby benefiting the broader scientific community and society. MathScy aims to impact education, society, and science by providing accessible mathematical tools, enhancing education with new teaching methodologies, boosting industries reliant on complex modeling, and promoting inclusivity by collaborating with diverse institutions including high schools, universities and technical colleges serving underrepresented groups. The project will empower scientists in diverse areas of theoretical and applied mathematics, fostering collaboration to address problems in Applied, Combinatorial, and Computational Algebraic Geometry, and generating, proving, or disproving conjectures.<br/><br/>Technically, the project aims to create a compositional and modular system using fine-tuned Mixture-of-Expert LLMs for mathematical reasoning, integrated with on-demand access to external mathematical tools. The system will incorporate domain-specific human feedback and intuition into the AI-assisted discovery process, generating human-understandable explanations of the AI's reasoning steps. Additionally, the project will develop new standardized representations, datasets, and challenging problems tailored for benchmarking and advancing mathematical reasoning systems. These techniques will be evaluated on significant open problems in mathematics and theoretical computer science, focusing on areas such as Applied, Combinatorial, and Computational Algebraic Geometry. The project will improve AI’s mathematical reasoning capabilities through techniques in mathematical language processing and knowledge assimilation, enhancing conjecture discovery, proof search guidance, and counterexample identification. Leveraging AI and formal methods, this research aims to address problems in these fields and their applications to STEM sciences. This comprehensive approach together with a committee of experts will ensure that the resulting system is robust, scalable, and capable of handling complex mathematical challenges.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
