Abstract: We will explore the potential for AI to accelerate mathematical research in various phases, except for experimental mathematics. This talk will include considering the accessibility and functionality of proof assistants, and discussing insights from Tim Gowers, Terence Tao, and others. We should also be able to look at some concrete examples. There will be time at the end for discussion.
Abstract: Scientific modeling and computation traditionally rely on structured mathematics and hand-designed algorithms. In this talk, I propose a new perspective: treating both modeling and computation as processes operating within the space of natural language. I will introduce two complementary approaches that realize this vision. The first uses symbolic learning based on tree structures to generate mathematical expressions, where modeling is performed by constructing symbolic trees and computation is governed by operator rules. The Finite Expression Method (FEX) exemplifies this approach by discovering interpretable, high-accuracy solutions to PDEs and physical systems. The second approach employs large language models (LLMs) for automatic code generation and reasoning to translate scientific problem descriptions into formal mathematical models and executable solvers to solve these problems. As an example, the OptimAI framework demonstrates how multi-agent LLM collaboration enables reliable end-to-end optimization problem modeling and solving. Together, these methods point toward a unified paradigm where symbolic and language models form the foundation for interpretable, scalable scientific discovery and computation.
Abstract: We will schedule two 20-minute talks per meeting to stay focused. The seminar will broaden its scope within AI and math, including concrete investigations, reporting on the state of the field's progress, history, philosophy, language, and even preparing for quals.
Abstract: Two 20 minute talks. The lack of creativity seen in ChatGPT is not due to the nature of AIs. Game-playing AIs like AlphaZero have an architecture that promotes creativity.
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