Any significance to why a lot of big names in AI have math PhD? I've been looking into AI research and I've noticed a nontrivial amount of individuals either received a PhD in math or had advisors who received a PhD in math. Some names include (Ben Goertzel, Marvin Minsky, Jürgen Schmidhuber).

I can see how a formal (arguably more difficult) training in math would help tackle issues in AI, but it'd make more sense to do a PhD in AI if one wants to make a career studying AI, no?

In contrast, all the high impact papers for top machine learning conferences (KDD, ICML, NIPS) were mostly from CS labs, but I cannot say that this is the norm in other AI subareas.

Is it actually better to do a PhD in math and do research in a topic that converge with AI?
All computer science is born out of Math.  The are a lot of computer programmers, web designers and the like who may not have math background, but they do not count as as computer scientist.

AI and other machine learning is all based on Math and statistics, so even going for a PhD in AI would mean that would have to learn a significant amount of math anyway.