An interdisciplinary symposium at the Simons Center brought together mathematicians, physicists, and AI researchers to examine how artificial intelligence is changing the landscape of scientific research, from mathematical proof and understanding to discovery and education.
On October 30, 2026, the Simons Center for Geometry and Physics (SCGP) at Stony Brook University hosted Math, Physics, and AI: 200 Years Later, a symposium exploring one of the most consequential questions facing contemporary science: How will artificial intelligence transform the way mathematics and physics are conducted?
Bringing together researchers from mathematics, physics, and artificial intelligence, the event examined the opportunities and challenges presented by rapidly advancing AI technologies. Through a series of research presentations and panel discussions, participants considered not only what AI systems can accomplish, but also what their growing capabilities mean for the fundamental processes of scientific inquiry: formulating questions, developing proofs, understanding complex ideas, and making new discoveries.
The symposium was organized around three interconnected themes—proof and understanding, discovery in mathematics and physics, and research and education—providing a framework for examining both the practical applications of AI and its broader implications for the future of scientific work.
Mathematical Frontiers and Open Questions
The afternoon began with a series of research presentations highlighting challenging problems at the forefront of contemporary mathematics and mathematical physics. The talks offered a glimpse into the range of questions being explored by the participating researchers, spanning geometry, topology, algebra, and combinatorics.
Ernesto Lupercio of Cinvestav opened the program with a presentation on complex structures on the six-sphere, followed by Michael Douglas of Harvard University’s Center of Mathematical Sciences and Applications, who discussed the moduli space of complex structures on the six-sphere. Sergei Gukov of Caltech presented work on the Hadamard maximal determinant and the Snake-in-the-Box problem, while SCGP Director Ludmil Katzarkov addressed the Shafarevich conjecture.
The program continued with Leonardo Francisco Cavenaghi of the Institute of Mathematics and Computer Science in Sofia, who discussed the Kuznetsov conjecture, and Mohammed Abouzaid of Stanford University, who presented on the nearby Lagrangian conjecture.
Together, these presentations illustrated the diversity and depth of problems confronting mathematicians today. They also provided a concrete research context for the symposium’s central questions about AI: How might emerging computational tools contribute to problems that have resisted traditional approaches? How can researchers evaluate the reliability of AI-generated results? And what distinguishes finding a solution from understanding why it works?
Proof and Understanding
The second part of the symposium opened with remarks from Stony Brook University President Andrea Goldsmith and Executive Vice President and Provost Carl Lejuez, who welcomed participants and introduced the afternoon’s broader discussions.
The first panel, Proof and Understanding, brought together Mohammed Abouzaid, Yakov Eliashberg of Stanford University, Bogdan Georgiev of Google DeepMind, John Pardon of the Simons Center, Vasily Pestun of Renaissance Technologies, and Vincent Della Pietra of Renaissance Technologies. The discussion was opened by Georgiev. At the heart of this conversation was a fundamental question: What does it mean for a mathematical result to be understood? As AI systems become increasingly capable of generating solutions and constructing proofs, the distinction between producing a correct result and developing a deeper understanding of its underlying ideas becomes particularly important.
Mathematical proof has traditionally represented more than a demonstration that a statement is true. It provides a logical framework through which mathematicians can understand why a result holds, identify the principles behind it, and build upon it to develop further ideas. The emergence of AI tools capable of assisting with mathematical reasoning raises new questions about how proofs are constructed, verified, and ultimately understood by human researchers.
Discovery in Mathematics and Physics
The second conversation, Discovery in Mathematics and Physics, expanded the discussion to the role of AI in generating new ideas and advancing scientific knowledge.
Participants included Michael Douglas, Ernesto Lupercio, Nikita Nekrasov and Zohar Komargodski of the Simons Center, Leonardo Rastelli of Stony Brook University, Sergei Gukov of Caltech, and Ahmed Almheiri of the SCGP and NYU Abu Dhabi. Lupercio opened the discussion.
Mathematical and physical discovery often begins with identifying unexpected patterns, recognizing connections between seemingly unrelated problems, or developing new approaches to questions that have remained unresolved. AI offers the possibility of accelerating aspects of this process by analyzing large amounts of information, identifying patterns, and suggesting relationships that might otherwise be difficult to uncover.
At the same time, the use of AI in fundamental research raises important questions about the nature of discovery itself. Can an AI system do more than identify patterns or reproduce known techniques? Can it suggest genuinely new mathematical ideas, or help researchers recognize connections that lead to entirely new directions of inquiry? And how should scientists assess the significance and reliability of discoveries made with the assistance of these tools?
The discussion brought together perspectives from geometry, mathematical physics, and theoretical physics, reflecting the increasingly interconnected nature of these fields and the potential for AI to influence research across disciplinary boundaries.
The Future of Research and Education
The final panel, Research and Education, turned to the implications of AI for the next generation of scientists and the institutions that support scientific research.
Moderated by Lisa Carbone of Rutgers University, the conversation included Bogdan Georgiev, Ernesto Lupercio, Christina Sormani of the CUNY Graduate Center and Lehman College, Lav Varshey of Stony Brook University, and Jacob Tsimerman of the University of Toronto and Lauren Williams of Harvard University, who participated remotely.
As AI tools become more widely available, their influence on mathematical education and research training is likely to be substantial. Students and researchers now have access to systems that can assist with calculations, explain concepts, generate code, and help explore mathematical problems. These capabilities offer new opportunities for learning and collaboration, while also raising questions about how mathematical knowledge and independent problem-solving skills should be developed and evaluated. For educators, the challenge is not simply determining how to incorporate AI into the classroom, but considering how mathematical education should evolve in an environment where some traditionally time-consuming tasks can increasingly be delegated to computational systems. For researchers, the question is how to use these tools productively while preserving the creativity, critical judgment, and deep conceptual understanding that drive scientific progress.
The three panel conversations were followed by a joint discussion, opened by Carlos Ruiz Alfonso, and an opportunity for audience questions, bringing the symposium’s central themes together.
Looking Ahead
The rapid development of artificial intelligence is creating new possibilities for mathematics and physics, but it also challenges researchers to reconsider some of the most fundamental aspects of their disciplines. The ability to generate a proof, identify a pattern, or produce a candidate solution is only one part of the scientific process. Understanding the underlying ideas, establishing the validity of results, and recognizing their broader significance remain essential to meaningful discovery.
By bringing together researchers working across mathematics, physics, and AI, the SCGP symposium provided a forum for examining these questions from multiple perspectives. Its combination of concrete research problems and broader interdisciplinary conversations reflected the importance of engaging with AI not simply as a technological development, but as an evolving influence on the practice and philosophy of scientific research.
As these technologies continue to advance, the relationship between human insight and artificial intelligence will undoubtedly remain an important subject of discussion. The symposium offered an opportunity to consider that future together, with an emphasis on the enduring values of mathematical inquiry: curiosity, creativity, rigor, and the pursuit of understanding.
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