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The AI Research Assistant: Promise, Peril, and a Proof of Concept

Tan Bui-Thanh, Professor, Oden Institute for Computational Engineering & Sciences

Abstract

"Can artificial intelligence truly contribute to creative mathematical research, or does it merely automate routine calculations while introducing risks of error? We provide empirical evidence through a detailed case study: the discovery of novel error representations and bounds for Hermite quadrature rules via systematic human-AI collaboration.
Working with multiple AI assistants, we extended results beyond what manual work achieved, formulating and proving several theorems with AI assistance. The collaboration revealed both remarkable capabilities and critical limitations. AI excelled at algebraic manipulation, systematic proof exploration, literature synthesis, and LaTeX preparation. However, every step required rigorous human verification, mathematical intuition for problem formulation, and strategic direction.
We document the complete research workflow with unusual transparency, revealing patterns in successful human-AI mathematical collaboration and identifying failure modes researchers must anticipate. Our experience suggests that, when used with appropriate skepticism and verification protocols, AI tools can meaningfully accelerate mathematical discovery while demanding careful human oversight and deep domain expertise."

Biography

"Dr. Tan Bui-Thanh obtained his PhD in computational fluid dynamics at the Massachusetts Institute of Technology (MIT) in 2007. He was a postdoc at MIT and then a research scientist at the Oden Institute for Computational Engineering and Sciences, UT Austin. He was an assistant professor, and then an associated professor at Oden Institute and the Department of Aerospace Engineering and Engineering Mechanics, UT Austin. Dr. Bui-Thanh was a recipient of the Moncrief Grand Challenges Faculty Award in 2014 and 2019, of the Distinguished Research Award 2019, and of the NSF Career Award 2019. He has been keynote and plenary speakers at various international conferences and workshops.

Dr. Bui-Thanh is a computational engineer and applied mathematician (with applications in computational fluid dynamics, wave propagations, solid mechanics, plasma physics and geophysics) and his research spans across different areas of Computational Engineering, Sciences, and Mathematics including model order reduction, PDE-constrained optimization, high-order finite element methods, parallel computing, statistical inverse problems, uncertainty quantification, data reduction methods, and model-aware machine learning."