Both machine learning and quant. finance are extremely extremely competitive. Having a math Ph.d does not cut it. It is mostly irrelevant actually. For quant. finance, if you have top grades from a highly respected university, that might get you an interview, but I think to do well, you'd have to do months of preparation.

Machine learning is my field and I can tell you, nobody is desperate to hire some math Ph.d who never did anything with ML.