Does pure math research help CS PhD admission chances?

[ksa]

Hi all, long time lurker and first time poster. I am currently a sophomore at one of the best schools for pure math in the country and am relatively advanced in pure math, with a 3.95 GPA overall and graduate coursework in mathematical statistics. However my research experience so far is totally nil and I am not so far ahead at CS, though I am playing catch up big time, as I'm taking algorithms + data structures + ML this spring semester. So you can see how my lack of research is a problem when it comes to my goal: admission to a selective ML PhD program.

I am wondering if pure math research experience would be good experience to get for my PhD program app. This summer I have three options. First, I could do a finance internship where I walk away with some nice cash but do no research at all. On the other hand, I could probably do pure math research with a professor at my school. But I simply don't know enough CS to start research in CS this summer, so the third option is just to spend most of summer on MOOC-type stuff getting super far ahead in CS and trying to really crush the research game junior and senior year. What do you recommend?

[Icydubloon]

You can do ML without coding. Don't take the internship unless you need money. Doing pure math research is fine.