AMS Proposal

AMS Special Session Proposal
Artificial Intelligence in Mathematics
2027 Joint Mathematics Meetings (JMM)
Chicago, Illinois | January 12–15, 2027

Motivation

Artificial intelligence is rapidly transforming the landscape of modern mathematical research, particularly in areas where deep structural theories interact with large-scale symbolic and computational complexity. In recent years, machine learning, neural networks, symbolic AI, and data-driven computational methods have begun to reshape how mathematicians approach problems in algebra, algebraic geometry, arithmetic geometry, representation theory, mathematical physics, and related foundational disciplines.

A particularly important emerging direction lies in the development of mathematically structured AI architectures built directly from algebraic principles. Beyond conventional neural networks, researchers are now constructing new classes of models based on graded rings, graded modules, tensor categories, representation-theoretic symmetries, and geometric moduli spaces. These include graded neural networks, graded transformers, neurosymbolic algebraic architectures, and geometric learning systems on weighted projective and moduli spaces. Such frameworks create a powerful bidirectional interaction: mathematics provides rigorous foundations for AI architectures, while AI becomes an instrument for discovering new mathematical structures, invariants, and conjectures.

These developments are especially significant in domains central to contemporary pure mathematics: automorphism groups of algebraic curves, superelliptic families, moduli of curves and abelian varieties, Calabi–Yau and toric varieties, arithmetic invariants, isogeny problems, and geometric structures arising in mathematical physics. At the same time, algebraically grounded AI methods are beginning to influence cryptography, homomorphic encryption, formal verification, and symbolic theorem proving.

This proposed special session continues and expands an active research initiative developed by the organizers through several successful prior events in this area. In particular, it builds upon:

• the first two conferences in the Artificial Intelligence and Mathematical Sciences (AIMS) Conference Series, organized under the International Association for AI and Mathematical Sciences (IAIMS), which have established an international forum dedicated to defining the frontier of AI and mathematics; and

• the AMS Special Session “Artificial Intelligence in Mathematics”, organized by the proposers at the 2024 AMS Spring Central Sectional Meeting, held at the University of Wisconsin–Milwaukee on April 20–21, 2024.

These previous meetings demonstrated strong international participation and confirmed the emergence of a growing global research community focused on mathematically rigorous AI and AI-driven mathematical discovery.

The purpose of this session is to bring together mathematicians, computer scientists, and interdisciplinary researchers working at this frontier to present recent advances, exchange ideas, and build collaborations. Particular emphasis will be placed on algebraically grounded AI architectures, graded neural systems, geometric machine learning models, and explicit computational results in algebra, algebraic geometry, arithmetic geometry, and mathematical physics.

By convening researchers across these interconnected fields, this session will strengthen an emerging international research network and help establish the Joint Mathematics Meetings as a leading venue for the future development of AI-driven mathematics.

Topics

Suggested topics include, but are not limited to: 

• machine learning and automorphism groups of algebraic curves; 

• AI methods for superelliptic families of high-genus curves; 

• arithmetic in moduli spaces via machine learning; 

• data analysis of Calabi–Yau hypersurfaces using weighted heights; 

• machine learning and isogenies of abelian varieties of dimension 2 and 3; 

• AI approaches to toric varieties and algebraic geometry; 

• artificial intelligence and Galois theory; 

• neurosymbolic learning and algebraic structures; 

• graded neural networks and graded transformers; 

• algebraic architectures based on graded rings, graded modules, and tensor categories; 

• geometric AI on weighted projective varieties and moduli spaces; 

• neural networks and invariant theory; 

• homomorphic encryption, graded rings, and AI applications; 

• formal proofs, theorem proving, and AI-assisted symbolic verification; 

• mathematical physics models inspired by algebraic and geometric AI frameworks; 

• and emerging applications of AI in pure mathematics grounded in algebraic and geometric structures.

Organizers

• Lisa Carbone, Professor of Mathematics, Rutgers University
  An internationally recognized expert in algebra, Lie theory, and representation theory, whose work on deep algebraic structures brings foundational strength to the mathematical architecture of symmetry-aware AI systems.

• Eric Ramos, Stevens Institute of Technology
  Researcher in algebra, combinatorial structures, and computational mathematics, contributing expertise in computational experimentation and AI-assisted mathematical exploration.

• Tony Shaska, Department of Mathematics and Statistics, Oakland University
  Organizer of the AIMS Conference Series and researcher in algebraic geometry, arithmetic geometry, computational algebra, and algebraically structured AI systems, including graded neural architectures. Founding Editor of the new Journal of Mathematics and Artificial Intelligence. 

Speakers (Tentative)

Artificial intelligence in mathematics is a rapidly emerging field, and the community is still developing internationally. The organizers are continuing to extend invitations through the proposal deadline. 

Significance to the AMS Community

Artificial intelligence is becoming one of the most important new methodologies influencing foundational mathematical research. This special session addresses a rapidly expanding frontier by bringing together researchers developing mathematically principled AI frameworks rooted in algebra, geometry, and graded structures.

Its distinctive contribution lies in emphasizing algebraically rigorous AI architectures—especially graded neural networks, graded transformers, and geometric learning systems built on deep algebraic structures—which represent one of the most promising new directions in the interaction between pure mathematics and artificial intelligence. This session will help establish a sustained AMS platform for this emerging field and ensure that the Joint Mathematics Meetings remain at the forefront of mathematically grounded AI innovation.