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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?

  • On a related note: the stack exchange site for artificial intelligence is now in beta. Feel free to join them and participate. – clueless Aug 19 '16 at 21:22
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    Unfortunately, machine learning will never need the mathematics I'm currently studying. -- [citation needed] – JeffE Aug 20 '16 at 3:49
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    Maybe so, but last I checked, Yann didn't own a time machine, so how would he know? – JeffE Aug 20 '16 at 15:23
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    I agree with @JeffE's comment. The quoted statement is so strong that I can't see how anyone without preternatural perception of the future could make it convincingly. You don't seem to mean it either: you go on to say that you are not interested in certain branches of ML (not the same thing at all!) and then in comments you say "will not be necessary for ML" (not the same thing at all!). If you mean that you don't want to pursue applications of D-modules and perverse sheaves to ML, please say that. – Pete L. Clark Aug 21 '16 at 0:14
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    Bottom line: it sounds like you are interested in two things and are not interested in pursuing a synergistic, "more than the sum of its parts" relationship between the two. So what that means is that your work on one of the two subjects has to be good enough on its own, and your work on the other will be tolerated / mildly appreciated as something extra you are doing. Many academics (in particular, many mathematicians) function this way. – Pete L. Clark Aug 21 '16 at 0:15
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I think you are correct in your estimate that doing ML work that requires only basic knowledge of mathematics probably won't get you hired, promoted, or tenured in a mathematics department.

The best I can say is this: If you publish enough in your pure math area for hiring, promotion, or tenure, then doing additional ML work can be a plus. Interdisciplinary work and public outreach could be emphasized at your future institution.

The other possibility would be getting a job in industry related to ML, and giving up on your pure math career. A Ph.D. in math, even in an unrelated field, may be useful for getting hired at such a place.

  • Regarding the job opportunity in private institute like Google, I'm pretty optimistic. But if that will mean giving up on my pure math career, it's a tough choice. Thank you for your advice. – Math.StackExchange Aug 19 '16 at 21:12
  • @Math.StackExchange: In your question, you wrote "I'm interested in neither something like application of algebraic topology to ML, nor industry after graduation." Above you mention your interest in working for Google. I'm confused. – Pete L. Clark Aug 21 '16 at 0:17
  • Google, Facebook and a few other big tech companies have exceptional research groups for ML such as that of DeepMind. As far as I know from their publication, their research activity is on the line of other major research groups in academia. It seems it is usual that some leading researchers in this field belong to such private research groups as well as those of universities. By "industry", I should've instead said "non-academic job". I apologize for that. – Math.StackExchange Aug 21 '16 at 1:12
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    @Math.StackExchange: It sounds like what you really meant by "industry" was "non-research job". Many industry jobs involve research, and not all academic jobs do. – Mark Meckes Aug 22 '16 at 14:34
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It looks like you found a new hobby. Congratulations. Have fun exploring that field. Why care about how closely related it is to your current work? If you are interested in it, just do it.

I bet every professor of yours has some hobby that is not directly related to what they are teaching/researching. There's nothing wrong with that. Not every activity in life is supposed to earn you a degree or build your CV.

  • A hobby can be mentioned on your CV, which could make potential future employers (in industry or academia) aware that you are interested in other things besides pure math. This is more of a workplace related issue I guess, so I just leave it here as a comment. – clueless Aug 19 '16 at 21:33
  • I hope my engagement in ML will not exceed the realm of hobby; otherwise, the obsession will distract me from finishing PhD. – Math.StackExchange Aug 20 '16 at 1:24

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