Generative AI just can’t do math – so let us use it !

Generative AI is abysmal at logical reasoning – as it was never designed to do that. But it is incredibly powerful and useful for many other tasks. Our students will use it, with or without our guidance. It is our duty to help them become more fluent and more savvy at employing such AI as students and in the future workplace. For over 2 ½ years, I have, initially sparingly, but recently much more vigorously, used generative AI in upper division math classes to address a common problem: As hard as it is to get students to volunteer to present (drafts of their) writings, most peers of the presenter routinely hold back at critiquing the presented work as they do not want to “hurt the presenter’s feelings.” Generative AI does not address the first item (our students need learning how to present, need practice) but generative AI is amazing at getting the entire class to viciously dissect every line of AI-generated arguments. This meets one of the curriculum’s central objectives, namely, that students learn, on one side, to identify mistakes and, on the other side, learn to have confidence in the correctness and soundness of their arguments even when there is neither a solution manual nor any grader providing external feedback. On the societal level, this strategy also develops a critically needed sense of skepticism in an age of ubiquitous misinformation: Distrusting everything is suicide. Instead, we develop a sense of a dividing line between where generative AI may be very helpful and where one need not to worry, and where generative AI likely will just be plain lying, making things up, “hallucinating”. Most of our examples come from the classes MAT 300, MAT 371, MAT 410 (Topology) Classes like Discrete Math, Combinatorics, Graph Theory etc. are very similar, but we also have hilarious examples from calculus I, and Math Circles for High school students.

---
For a preview and to prepare for more discussion, you are welcome to visit the preprint "ChatGPT and AI Enhancing Undergrad Math," which is to appear in the Proceedings of the 30th Asian Technology Conference Mathematics, Manila,
Philippines (2025).  https://math.la.asu.edu/~kawski/preprints/atcm25-final.pdf