RTG: Mathematics & AI Synergies (MAIS): Algebra and Applications

Artificial intelligence (AI) is rapidly transforming science, technology, and everyday life, yet many of its most powerful tools operate as "black boxes" whose decisions are difficult to interpret or trust. This project will train the next generation of mathematicians to address this challenge by developing a deeper understanding of how AI systems work and how they can be made more reliable and transparent. Based at the University of Wisconsin-Madison, the program will support a community of undergraduate students, graduate students, and postdoctoral scholars through research experiences, mentoring, courses, and workshops. Participants will gain skills at the intersection of mathematics and AI, preparing them for careers in academia, industry, and the public sector. By increasing participation in the mathematical sciences and strengthening workforce development in data-driven fields, the project will contribute to national needs in technology, innovation, and education. The project will advance research at the interface of algebra, statistics, and machine learning, with an emphasis on developing mathematical foundations for interpretability, identifiability, and robustness in AI systems. The research will investigate how algebraic and geometric structure can be used to analyze modern AI and machine learning models, including neural networks and latent representation models, with the goal of improving reliability, transparency, and uncertainty quantification. Core research areas include algebraic statistics, tensor methods, parameter estimation, and high-dimensional inference, with particular emphasis on provable guarantees for representation learning and model recovery. In parallel, the project will investigate AI-enabled approaches to mathematical discovery and scientific computing, including automated reasoning, human-AI collaborative workflows, and machine learning methods for large-scale computational problems. Vertically integrated training will connect participants across career stages through coordinated activities such as research assistantships, summer programs, and thematic courses. These efforts will foster interdisciplinary collaboration and generate new mathematical theory, computational tools, and educational materials. The project will strengthen the role of algebra in modern data science and produce broadly disseminated outcomes, including scholarly publications and innovative curricula, that advance both mathematical knowledge and AI technologies. 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.