I'm a pure math (geometry/topology-oriented) PhD student at a top-level American university. I recently got interested in machine learning and read the recent papers. Unfortunately, machine learning will never need the mathematics I'm currently studying. There are some branches of machine learning which require some sophisticated mathematics, but I'm interested only in the mainstream of ML (as well as the pure math topics I'm currently studying), which requires only the basic knowledge of mathematics. I'm interested in neither something like application of algebraic topology to ML, nor industry after graduation. 

It seems that most pure math PhD students and professors aren't interested in such unrelated subjects. If I will do research on ML with EECS students or professors, I suppose I will be considered as unproductive. 

I was wondering if you would give me an advice me, so that I can continue studying the both subjects without having to be worried?