- Solve a quadratic equation: Correct answer, and I like the explanation
- Compute the eigenvalues of a 2×2 matrix: Correct answer, although the solution isn’t my preferred approach–it relies heavily on formulas (the characteristic polynomial of a 2×2 matrix, the quadratic formula)
- Is the function x goes to x squared injective? Answer and give a proof. It gave the correct answer. I like some aspects of its output (for instance, that it started with the definition of injectivity, and it showed its “scratch work” as it “thought through” the answer), but the total output is much longer than I wanted to see.
- Find an automorphism of the Klein quartic. Here ChatGPT gave a response that sounds completely confident, but the formula it gave, $(x,y,z) \mapsto (\zeta_3 x, \zeta_3^2 y, z)$ is incorrect; it does not preserve the Klein quartic. My hunch is that ChatGPT found a source describing this map as an automorphism of the Fermat cubic x^3+y^3+z^3=0 and didn’t know that it couldn’t simply present it as an automorphism of the Klein quartic, too.
Taken together, these four examples suggest to me that ChatGPT (and AI in general) are exciting tools that may already be good at solving and explaining lower-level math problems that have many published solutions, but perhaps at this moment they are not as good when it comes to more advanced questions with fewer published solutions.
Let’s make time this fall for discussions about the impact of AI on how we teach our math classes. If you are interested in trying out AI but haven’t done so yet, let’s chat. You’re exactly the group my committee is trying to reach–I’d love to hear how we can help you.
The Faculty AI Interest Group is a collaborative effort between the faculty and the Educational Technology and Research Computing team of the Office of Information Technology.
The goals are to:
- Keep abreast of AI development in general and Generative AI – GAI – in particular and their impacts on education, teaching and assessment
- Provide a forum of dialogue and exchange of information between the faculty and IT
- Review, research, and explore AI tools in education
- Explore interdisciplinary experimentation of upcoming AI tools and applications in teaching, learning, and research
- Host an Information clearinghouse, awareness raising, workshops, training, and more