The project of Artificial Intelligence has to a large part been driven by questions like: Can “AI” play chess? Can “AI” take legal decisions? Can “AI” write poetry? How about maths? Intriguingly, while LLMs on the one hand have appeared to come up with correct solutions to hard Math Olympiad problems, at the same time ChatGPT famously failed to “count” the correct number of “r”s in “Strawberry”.
In the history of mathematics, there have been several attempts to mechanize (parts of) mathematics. The arrival of LLMs gives a new reason for reflecting on how the structured language in which we do mathematics relates to the substance and practice of mathematics, but also on how language, abstraction, thought, form and meaning connect (for us). What can or should the role be of LLMs in mathematics research? Are LLMs going to be rivals to mathematicians, as much as they are currently presented to be for lawyers and coders? In this talk I will take a humanities-centered perspective on mathemathical research, building on my own background in intuitionistic mathematics, the Eindhoven Automath project, and reflecting on the recent “Leiden Declaration” about LLMs in mathematics research. I may conclude that mathematics is more like poetry than like chess.
Author: Francien Dechesne