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I have a master in physics and philosophy and have a keen interest in mathematics. Currently I am doing a PhD in philosophy. On a personal level, however, I cherish the interdisciplinary ideal of combining mathematics, physics and philosophy. I am well aware that realizing this ideal requires an enormous amount of work and talent – and that very likely I cannot 'completely' realize it.

On a structural level, I suppose this is an unfortunate side-effect of the level of specialization in academia today. On a subjective level, however, I feel the need to “revolt” against such over-specialization. It a shame that some "philosophers of science" in my branch haven't solved one differential equation in their life; yet they intend to reflect on what physicists do. I am convinced that combining different disciplines is a worthy thing to do. I suspect many people would agree with me, but the competitive reality of academia makes it very hard to realize.

The time one invests in a secondary area of interest (i.e. mathematics, physics) takes away time to do research in one's main area (i.e. philosophy). The reduced time would (on the short-term) make me less productive and successful. However, in the long-term, it might allow me to produce work of more value and depth.

  • (1) Is it wise for a PhD student, somewhere below on the academic ladder, to gamble already on long-term investments, or should one give in to the short-term safety and (over)specialize in one area?

  • (2) Is there some middle-way between the two extremes?

  • (3) Is it more useful in later stages of one's career to have a broad skill-set or have more publications in one (limited) area?

  • Philosophy of Math and Philosophy of Science are both valid subfields of philosophy, though I don't know how active they are. You certainly can find universities with interdisciplinary committees related to those topics. You may not be the guy running the experiments or doing the proofs, but you can be a component in something broader. As an undergrad I worked on a project with a philosophy prof, a psych prof, and a computer science prof (cognitive science committee) once. Look around a bit. – LinearZoetrope Jan 3 '15 at 13:12
  • " I am well aware that realizing this ideal requires an enormous amount of work and talent – and that very likely I cannot 'completely' realize it." --- why?! What's so enormous about it? I mean, if you want to be a world-class mathematician and a world-class philosopher, then it seems hard. If you are O.K. with a "decent" level of a professional mathematician, physicist and philosopher, this is completely realistic, with plenty of people having accomplished that. (I do have high standards, though. :-) – user14102 Jan 3 '15 at 23:46
  • (1) It is not wise, but people do such things all the time, and you can do it too. For Christ's sake, there are 800 million people starving. People sometimes risk their lives. Think about it. – user14102 Jan 3 '15 at 23:49
  • (3) The world is changing so much, that nobody can tell. – user14102 Jan 3 '15 at 23:49
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I think this is a good question, but I have only a brief, partial answer: you may have to accept that, in pursuing the interdisciplinary topics that interest you, the time and energy you spend will not be repaid with any kind of academic currency, but only in less tangible forms. In other words, you may never get a better job, get an extra paper published, or even get an extra pat on the back from a colleague; but you may nonetheless, in a subtle and unsung way, advance the anti-specialization principles you espouse simply by doggedly producing quality work that embodies them. This may sound cynical, but I mean it seriously. Of course, you need enough tangible reward to keep your career going, but it sounds like you're asking about how or whether to invest the energy to go the extra mile above and beyond that. It's possible to derive internal comfort from believing that you're doing your best to produce the kind of work you think needs to be produced, even if doing so doesn't earn you any praise or advance your career in any concrete way. In the end, whether you continue to do this work will depend on whether you can be happy and sane doing it, and drawing strength from your inner conviction, rather than from external validation, can help with that.

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    I would upvote this answer ten times if I could :-) – Aubrey Jan 2 '15 at 20:22
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    Re: "happy and sane": I do not have any proof for it, only my (and not only mine) belief, but doing anything beyond one's narrow specialized field is a good way to preserve sanity in academia. – mbork Jan 7 '15 at 1:13
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Good question, but likely to be closed as "opinion-based" or "too broad". My (opinion-based) take below.

Career-wise, you can likely luck out or strike out with either approach. You can turn into the world's foremost expert on a teensy, tiny special sub-sub-sub-field. If this turns out to be an important field for the next decades and your reviewers like it, then you are in luck. However, every subfield will likely be sucked dry at some point in time, so even the most specialized specialist will need to switch fields, methods or something else at least at some point in their career. Suppose you were the world's top expert on some obscure topic sexy in 1985, as a freshly-minted Ph.D. - I don't think this will still be quite as hot today. So a one-trick pony will need to switch tricks now and then.

Note that you need some consensus in your field that your one trick at the moment is actually hot. It's bad if you write a grant application and your reviewers groan "not again; he's been milking this particular technique for ten years now, when will he finally stop?"

Alternatively, you can do what you seem to prefer: become proficient in multiple connected fields. This will mean that you won't be the mother of all experts in any of them. But you may just become the person who can actually see, explain and analyze the connections between these fields. Given that there is more and more emphasis on interdisciplinary research these days (which I'd say makes a lot of sense and likely is here to stay), you are well placed to become the linchpin getting disparate single-topic experts together to write grants or papers.

Of course, you still need to pick fields that actually have some connection with each other. You may be interested in all of Shakespeare's plays, high-dimensional complex geometry and parallelized software development, but it will be hard to bring these disparate strands together into a coherent whole.

So you will again need to impress reviewers that your combination makes sense. If your interdisciplinary approach is reviewed by focused experts, these may not appreciate what they perceive as "no expertise" in your research.

(Incidentally, by beautiful wife goes the second route. She is likely not the world's greatest geneticist, nor the world's greatest clinical psychologist or therapist, but she does pretty good interdisciplinary research on the genetics of certain psychological conditions and their therapy. Among other things. She started this type of jack-of-multiple-trades approach after her Ph.D.)

I have seen the metaphor of "T-shaped people": people who have a limited understanding of a lot of things (the horizontal bar of the T), but are experts in depth in at least some particular topic (the vertical bar). This is the ideal my employer wants us to strive for - we should neither be "I-shaped" (all expertise, no general knowledge) nor "minus sign-shaped" (all general knowledge, no expertise). This makes sense to me.

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    Thanks for your excellent answer. But I get the feeling that OP would be interested in whether it is practical/valued to be a π-shaped person. And if not, I would :) – Eric Stucky Jan 3 '15 at 12:04
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I have found that a middle-of-the-road approach works best. Scientifically minded individuals tend to be perfectionists. While it is important to pay attention to details, perfection does not exist and life is short. Keep your eye on the prize and make your mark on the world but don't forget to have a life.

Read some of the books about Richard Feynman. By all accounts a genius but by his own admissions said he was mostly like others but had developed a few special "tools" or ways of looking at a problem. So yes, explore avenues that may not have immediate rewards but may have value for the future. Great discoveries are often overlooked by the unprepared mind...

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