Mathematicians Discuss Rigorous Illustration and AI's Impact on Mathematical Practice

Workshop on Mathematical Meaning

In January, a workshop at the Institut Henri Poincaré (IHP) brought together mathematicians, historians, artists, and educators. The focus was on the meaning of mathematical illustration and what constitutes a rigorous illustration within mathematical research. This event was part of a special trimester dedicated to the use of illustration in mathematical research.

AI's Influence on Mathematical Practice

The discussions at the workshop became more urgent due to recent advancements in AI, which have prompted questions about the fundamental definitions of human mathematical practice. Participants explored how AI impacts the traditional emphasis on theorem production as the primary measure of success in mathematics, arguing that understanding is a more crucial, though harder to measure, aspect.

Redefining Mathematics Beyond Proofs

Bryna Kra notes that AI has diminished the scarcity of deep theorems, which previously served as reliable indicators of deep thought. Silvia De Toffoli and Eamon Duede reject the idea that mathematics is merely a game machines can win, asserting that it is a body of knowledge engaged with and interpreted by a scholarly community. Matilde Marcolli suggests that the focus on big theorems was a community choice that can be re-evaluated.

Publication and Future Directions

The insights from these discussions culminated in an article, written during the summer in the context of the Leiden Declaration, which has been accepted for publication in the Notices. This article explores how mathematical illustration, including computer graphics, represents an activity of human mathematicians that extends beyond traditional proof-writing, offering insights into the future direction of mathematics.