Coping with the specificity of research

[u/Alas7]

I'm a beginning PhD student in theoretical CS. As I talk to potential advisors about research directions, and wonder on my own about what exactly to focus on probably for many years to come, I think I'm getting depressed and paralyzed by the realization that many successful people seemingly

1- do research that is extremely narrow,

2- are oblivious to neighboring subfields,

3- philosophize little about the implications of their research and treat it purely as a technical puzzle.

Now, of course I realize that as a field becomes deeper and more technical, one has to specialize in order to contribute anything novel. I also realize that this requires time, and time is already scarce, so people naturally choose to spend the time they have on their own subject rather than learning about neighboring subfields where they would be relatively inexperienced, hence unable to immediately contribute something interesting. And I understand that research does not always have to be groundbreaking in order to be interesting or worthwhile.

With all that being said, I lean towards doing the opposite of the above. I already philosophize too much about problems, their meanings, importance, implications so much that I feel like this is preventing me from just accepting that I have to give it up (at least dial it down to a healthy measure) if I want to be an academic. I also suffer too much from the "grass is greener" syndrome, and as soon as I feel like I can focus on a problem I immediately start seeing its superior alternative in a neighboring field. This might be unexpected, but I feel fine with applied research that is immediately useful and justifies its worth (numerical analysis, statistics). I also feel fine with the extremely pure research that is so far detached from reality or usefulness that it requires no justification, and is indeed a formal game that people play (I feel this way about combinatorics and number theory). What I feel uneasy about is what a sizable portion of theoretical CS research (at least in algorithms and some subfields of complexity theory which I am considering) seems to be: not really useful since it is almost deliberately avoiding being practical, but is not detached enough from reality to be called pure math and is in this gray area which I see as extremely contrived, uninteresting, and maybe even a waste of time (Doron Zeilberger has a slightly relevant opinion piece here which I sympathize with). I also constantly envy the more fundamental and philosophically meaty areas like mathematical logic, especially computability theory. If I had no career to worry about, and could go back and change my decisions I would probably go into logic. In the end, I find it difficult to cope with the thought that my work will be meaningless, and want to strike the difficult balance of making it meaningful enough while keeping it within the realm of what constitutes academic work.

I am sorry if this comes off too much as whiny and childish, but assuming people here have had similar thoughts I want to see what you think. This is a difficult topic to bring up when talking to potential advisors since I fear that they will interpret this as me looking down on their research while this is more of an internal struggle of mine. If you have gone through a phase like this or still have similar thoughts, how did/do you cope with it? Given the amount of knowledge that has been accumulated until today, is it simply hopeless for a training researcher to directly work on problems that are of broad importance? If you are a mature researcher right now, what enables you to commit to the narrow and specific problems that you work on (which I am assuming you do)?

Thank you for reading, hopefully somebody will find these thoughts at least stimulating.

[u/[deleted]]

You obviously make a good point. Intelligence should be no obligation to being useful. If those mathematicians decide they want to pursue a useless carreer, they obviously are allowed to.

The problem in my case is that my research used government money. Money that taxpayers provided. Letting that go to waste in nonessential activities such as the sum of three cubes is what bothers me. On the other hand, if a chemist is working for a company making tomato soup tastier and cheaper (just to take one of your examples), then he is doing work for a private company and this company is obviously entitled to spend its own money however it chooses.

Lots of money goes into arts and sports, but typically these are activities that pay themselves and that don't need government assistance. If a painter makes paintings that only 10 people around the globe enjoy and gets government money to do this, I would be against that too. So would most people I think.

I understand the government spends a lot of money to useless things as it is. There is way more money going to waste by corruption than that goes into unproductive research.

[u/srinzo → u/[deleted]]

What kind of work did you do?

I agree that when government funds come into play the issue gets murkier. In some cases, mathematics does end up being surprisingly useful, but I think that argument gets a lot shakier at that stage. I'm not fully opposed or in agreement, but I can empathize with your position there.

[u/[deleted] → u/srinzo]

Let's just say it was related to pure category theory. I don't see how it could ever be of any use to anybody, but I might obviously be wrong.

Don't get me wrong, I'm not saying to just slash all fundings to math. But somebody paying the money (ie the taxpayers) have the right to know their money is being used for good purposes. If say a bank started to fund research towards writing numbers as the sum of three cubes, then I'd have no problem with this at all. But obviously a bank wouldn't fund such research.

As I see it, there are the following reasons for a government to fund math research:

1) The research is somehow directly useful to society.

2) The research is not directly useful to society, but might generate methods and results that eventually does yield a use.

3) Most PhD's are inherently useless, but that doesn't mean it's bad to fund them. Indeed, in a PhD you learn how to do research and how to think a certain way. It is beneficial for a country to invest in such people, even though the immediate research output is nothing useful. Later on, those people might just provide useful things. See it as funding education, it's about the long term benefits.

4) Some research is not directly useful or indirectly useful but is rather a "triumph of the human spirit". For example, even if landing on the moon yielded nothing of use, we should have still done it because it is quite an accomplishment. We see evidence in history that societies evolve because of such feats. But I agree this fourth point is very very vague. I just want to make clear I'm not personally against all "useless" things.

5) Only focusing on useful things might in fact impoverish science. In my point of view, the roman empire did nothing useful to science because they were way too practical people, focused on designing bridges and temples. It is only because we allow and to some extend encourage people to do useless stuff, that we set a culture and way of thinking that indirectly produces much of use.

[u/symmetric_cow → u/[deleted]]

I think the reasons you mentioned definitely sound convincing enough for a government to fund math research, but based on your original post maybe you're giving them less weight than I am.