I think a similar question was answered in PhD Research under guide/advisor of a different department by JeffE. I’m asking a slightly different question. Yet if you find it identical to the above one, you can report it to be ‘duplicate.’

The deadline of math PhD programs I’m applying for is approaching and passing, but I guess asking this question isn’t too late. I’m interested in both pure math and machine learning, and I chose to apply to math PhD exclusively due to my background. However, recently I’ve been into developing an algorithm related to proof verification and others for application to mathematics using the state-of-the-art deep learning techniques. I’m certain most or all professors in math department I’m applying to (or anywhere else) aren’t working in such an approach, since that’s more of a job of professors in CS department. Though the answer may be case-by-case, is this kind of topic appropriate for my PhD thesis? I understand that I can have a co-adviser from CS dept., but is this topic likely to get accepted from math department? If so, by any chance if my interest totally shifts to machine learning proper and has nothing to do with mathematics at the late stage of my PhD, do I still have to work on something related to math in this sense? (I assume the answer is Yes.)