Feel dissatisfied after each submission

Question

I am a third year graduate student at a "top-20" university who works on fine-grained complexity (lots of playing with 3-SUM, OV and the usual popular hardness conjectures). I have been fairly productive over the last year or so and have 3 accepted papers and two submitted papers. All of this to say that I am a fairly experienced graduate student and what I am about to describe is not anecdotal.

Every submission brings me more dissatisfaction than satisfaction. Just before I start working on a problem, me and my advisor identify a list of concrete questions that need to be answered. After lots of thinking, we have some very nice non-trivial results which gives me a lot of happiness and satisfaction. As we start to write down all of the results, inevitably, there are some more interesting variants that pop up but are much harder to make progress on. After the initial euphoria point, I feel everything seems to go downhill. There are so many variants that also need to be answered, are clearly in the purview of the problem at hand but I am not able to. By the time we submit the paper, I am so dismayed that results in the paper seem almost trivial. Perhaps this is simply tunnel vision, but I can't overcome the sadness about not being able to answer peripheral questions (although these make for a terrific conclusion section).

This has happened every single time and I am wondering if this is a common feeling. Do other people in theory community feel the same way? I am not sure if this is an academia wide feeling. My fellow graduate students from other areas are over the moon after every submission (but this is just anecdotal).

Edit - I see that there is another soft-question on the front page. I apologize for adding another one. Its holiday season and (only?) after a few drinks, one starts to ponder over these things!

Answer 1

Yes, it is very common. Once we spent months thinking about a problem we start to see relations so well that the solution looks trivial to us. It is not specific to academia, once we have a solution for a problem it makes the problem look easier that it really was, all the clouds that prevented us from seeing it have disappeared.

How to deal with this feeling? I haven't figured out myself but a few observations that might help:

Remind yourself what seems obvious to you is not for many others. How many people in your broad area saw the solution beforehand?

For most results (and most results are not break through results) I think it is the case that someone else in our field who is smart enough could have figured it out as well. This also has an effect that we feel we are not so special after all. Well, we are not! Once we accept that there are others who are smart enough and deal with our ego and become humbler we tend to have higher satisfaction from our contributions. Yes, X, Y, and Z could have done it as well. But we were the person who put the effort to actually do it.

Another one is to pay more attention to what problem we decide to work on. Be very clear with yourself why you want to work on a problem. Don't do so just because it looks interesting or difficult or others say it is interesting. How would knowing the solution to the problem affect our understanding and world? If we are clear about that then the fact that the solution to the problem looks simple wouldn't bother us, it would delight us instead. This might be difficult though for a student, you have to pick a problem that is meaningful and solvable. It is harder in more pure areas than applied sides. And often we don't end up solving the real meaningful problem but make some meaningful advance towards it. Keep in mind that is also valuable. Even our failures can be valuable if we can share the insights we obtained from them with others.

There is also how others judge our contribution. It is will known some areas of theory have a problem of valuing technical heavy lifting more than some meaningful contributions. Don't let them discourage you. In the long term, most of those technical heavy liftings will be forgotten, don't allow the facade to discourage you from working on meaningful problems.

Lots of young researchers focus on proving themselves. Focus instead on building good and meaningful collaborations with others to work on meaningful problems. That is much more important in the long term. With some luck you will end up with some significant meaningful contribution.

Answer 2

You aren't alone, and it's not unique to theoretical CS, or even mathematics, or even this millenium.

Chaucer lamented in The Parliament of Fowls:

 The lif so short, the craft so long to lerne,
 Th’assay so sharp, so hard the conqueringe,
 The dredful joye alway that slit so yerne

 The life so short, the craft so long to learn
 The effort so sharp, so hard the mastery,
 The difficult joy always slips away so quickly

Hippocrates (yes, that Hippocrates) put it even more sharply:

Ὁ βίος βραχύς,
ἡ δὲ τέχνη μακρή,
ὁ δὲ καιρὸς ὀξύς,
ἡ δὲ πεῖρα σφαλερή,
ἡ δὲ κρίσις χαλεπή.

Life is short,
and art long,
opportunity fleeting,
experimentations perilous,
and judgment difficult.

Speaking as a Theory B person, the experience of complexity theory always struck me as being different in character from the experience one gets from semantics or type theory.

To me, it seemed like every problem in complexity required a genuine idea, so that if you modify the problem even slightly, then you need an entirely different new idea. In contrast, in semantics the hope is to solve problems by identifying the algebraic structures in play, in such a way that the solution become obvious -- there's no way not to solve it. (Benjamin Pierce once remarked that you know you have a good type system when all the proofs are boring.)

So when things are going well, complexity feels like you are in a creative conversation with mathematics itself -- you try something, and this suggests a new idea to you, and your response to that gives you yet more ideas. But when things are going poorly, you feel trapped, like you are doing an infinite sequence of puzzles which offer no insight into anything else.

When things are going well in semantics, you feel like you are touching the architecture of the world, like an x-ray showing you the very bones of mathematics. But when things are going poorly, you also feel trapped, like you are trying to fill out the world's most boring tax form.

My suggestion would just be to find some spare time to study some abstract algebra. It should satisfy your generality jones, and learning it is almost certainly beneficial to your research.

Answer 3

By the time we submit the paper, 
I am so dismayed that results in 
the paper seem almost trivial.

I'd argue that you had failed to solve the problem if it didn't seem trivial after completion!

The essence of science is the production of (novel) truth. The essence of truth is that it needs to be reproducible by anyone.

In the past the paradigmatic example for "anyone" was the slave boy in Plato's Meno's (1). Nowadays the highest standard of rigour requires convincing a mechanical proof assistant (2) that our solution is derivable (from the chosen foundations of maths). A proof assistant is, anthropomorphising a little, really dumb. In contemporary math and theoretical CS we take human peer review as a proxy for mechanical verifiability, i.e. truth, but work towards more mechanical proof checking, see e.g. (3, 4, 5). (Indeed, I doubt that you would be able to formalise your work for a proof assistant, without investing years of work.)

You would not have succeeded in doing rigorous science if each step of the solution wasn't trivial.

Of course this is not particularly helpful in getting rid of your worries, so maybe you stop asking yourself whether the work was worthwhile. Instead, ask others! In particular, ask yourself: how many others have tried to solve the same problem but failed. Presumably, your subfield of CS has a list of famous open problems, why not have a go at one of them? (Warning: chasing famous open problems is a good way to fail a PhD ..., so I recommend discussing this with your supervisor if you want to go that route.)

 me and my advisor identify a list of concrete 
 questions that need to be answered.

Chances are that your supervisor carefully considers whether the questions you work on are simple enough so that a PhD student can crack them with a few months of work (but difficult enough for publication).

1. https://en.wikipedia.org/wiki/Meno%27s_slave

2. https://en.wikipedia.org/wiki/Proof_assistant

3. https://www.quantamagazine.org/univalent-foundations-redefines-mathematics-20150519/

4. https://en.wikipedia.org/wiki/QED_manifesto

5. https://en.wikipedia.org/wiki/POPLmark_challenge