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At a panelist event that I attended recently, exactly 100% of the current students and alumni in the room who didn't have PhDs in Machine Learning stated that they wanted a PhD in Machine Learning -- and they all wanted to know how and where to accomplish this goal. I'm honestly not sure whether most of these students can even describe what machine learning is. There were long lines to talk with computer science PhDs, who are directors of research either at a university or in industry, e.g., Google, Goldman Sachs - everyone was so infatuated with the thought of getting into Data Science.

Does any field in the past compare to the current field of Data Science, in terms of trendiness and importance?

Was it Probability Theory? Fourier Analysis? Number Theory? Mechanics? Law School?

This coming semester, I really wanted to follow my interests and study measure theory and functional analysis - just skimming through the table of contents of the functional analysis book by Reed and Simon was pretty exciting in itself. Yet, it's hard to drown out the Data Science influence, and I feel that I should be "wiser" and take machine learning / data science courses instead.

A respected math PhD student in our department advised me that, "if you study some subfield of algebra deeply, then in the future perhaps a dozen people might understand your work. But if you get into Data Science, it's a field that's projected to grow for decades to come, and if you land in industry instead of academia, all of the skills are transferable, unlike the skills gained from studying algebra."

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    We should all aim to be celebrities? :) And, gosh, surely there's no hype in any of this! Whew! Lucky there's no b.s., ... :) Slightly more seriously, if you're talking to crowds of people who self-select for X, they will tell you that you, too, should go for X, because it's the only sensible choice. Noise has swamped signal in any such case. Aug 20, 2016 at 23:29
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    I assure you that there are rooms full of people 0% of whom want to get a PhD in Data Science. So it depends a lot on what the panel is. In general, the whole point of an academic career is that you get to spend the rest of your life studying what fascinates you. I'm not (at all!) recommending that potential PhD students think deliberately impractically, but if you're being primarily influenced by maximizing the number of people who can understand and the percentage of skills that transfer over...maybe pursue a nonacademic career. Aug 20, 2016 at 23:55
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    Also, getting a PhD in anything involves poking at the boundary of what is known in that field. So of course people who are getting their PhDs in Data Science are spending a lot of time thinking about things that are not of current interest to the majority of data scientists: they're going deep and specialized. Conversely, if you want to jump onboard doing Data Science in a broad, crowd-pleasing way: who says a PhD is necessary or helpful for that? Aug 20, 2016 at 23:57
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    if you study some subfield of algebra deeply, then in the future perhaps a dozen people might understand your work. But if you get into Data Science -- ...then in the future perhaps a dozen people will understand your work, and you won't be one of them.
    – JeffE
    Aug 21, 2016 at 3:30
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    Actually, if "everyone" seems to be interested in going into a field, it might be a sign that it's going to get saturated. This has happened many times.
    – user11599
    Aug 21, 2016 at 3:43

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Does any field in the past compare to the current field of Data Science, in terms of trendiness and importance?

Yes. It has happened before, it is happening now, and will again. There was programming in the 80's and 90's. Then Software Engineering... Back in the late 40's and 50's there was a big boom in nuclear physics, and nuclear engineering.

Don't get a degree because you think that there might be good jobs. Do what is interesting to you (and something that is likely to get you a job.) If you like Data Science, then do it. If you don't, then don't. you are going to have to live with doing the work all day, every day for many, many years to get a PhD. If you aren't in love with it, then you will not succeed.

Since a PhD is a long-term commitment, takes a lot of patience, costs a lot of money and takes a lot of time during the term, it is not to be undertaken by an answer on the internet. It is your decision.

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