Harnessing the ever-growing capabilities of contemporary computing systems for pushing the boundaries of knowledge is a central theme in modern science. Success stories include modeling complex quantum-mechanical systems and high-fidelity fluid-dynamics simulations in medicine, aerospace dynamics, and meteorology. Notably, most computational methods are developed for numerical approximations of complex systems, leaving higher-level tasks, such as symbolic manipulations, theoretical derivations, and algorithmic design, to humans. However, with the remarkable performance of modern AI methods in high-level cognitive tasks such as natural language processing and image generation, many believe that higher-level mathematical tasks are also within the reach of computational science and AI.
This theme explores the largely uncharted field of applying modern computational science and AI to discover new mathematics. In particular, we will apply advanced machine learning techniques to search for counterexamples in challenging analytic problems, gain new insights for arithmetic questions in algebra and number theory, and find optimal mathematical structures for digital twins of dynamical systems.
| Date | Event |
|---|---|
| March 1 | Application deadline |
| June 15 | On-campus REU phase begins |
| August 7 | Last day of on-campus phase |
Computational Science and AI for New Mathematics
To facilitate interactions across the teams and interactions between participants and faculty, our site emphasizes cohort activities. Those activities include:
We involve participants in planning these activities and adapt them based on their background knowledge and project needs.