The bar for math PhDs already ruled out like 99.9% of the population, so I don't see it having much effect on discouraging people. The gap between even a bright student who takes AP calculus or whatever and someone studying e.g. spectral sequences is already incomprehensibly large. Like you literally could not even convey to a smart young person how far away they are from the boundary of today's understanding. I don't think I even have a reasonable sense with a math bachelor's!

People who get into math do it because they can't not do it.

I think it'll become increasingly important to have folks thinking about how to explain new math in a way that makes sense to your math bachelors students. And to your bright AP Calc students.

If we can point ChatGPT at these problems and get eventual answers, that's awesome, but it'll still be important to figure out how to tell people why this matters in ways they understand.