the professor has all the power in the classroom. If you don't want cheating, define better conditions for the exam. You allowed a take-home exam which means students are able to use any and all resources.
They're going to have change everything so use of an AI assistant doesn't matter because once they graduate they're just going to continue using it anyway.
If it's a math for finance course then some kind of model building for the midterm and being marked on the quality of the model or something. If AI becomes so good that it always chooses the best fitting model and requires no numerical optimization then they will have to change the courses to be more like UChicago where it's primarily undergrad directed research but AI assisted.
Damn that's crazy. Guess the take home test is dead now.
I never understood this behavior from undergrads though, you're paying so much for an education and then you just skip the education part? Why bother?