Others had said it better than I will, but let me share my own experience.
In the past, when I was working on my PhD, I felt that pressure quite hard. But it was not a “moral” pressure like yours: it was a “material” one. If I couldn’t find something enough interesting to be named a PhD thesis, I wouldn’t be a mathematician at all.
That was an awful feeling: working with that feeling in the back of my mind was the worst thing I could have done. In the end, after some years of suffering, and changing my thesis advisor, the thesis was written. I have to credit my second advisor for it very much. But also, I guess, because without noticing it, I just forgot my fears and began to enjoy the maths I was doing for the sake of it. Because the problems I was facing –and eventually solving, some of them- where great fun!
My career as a math researcher has had its ups and downs after that, but the best moments are always when and I have fun doing it: reading papers from other colleagues, studying books to learn a new subject, writing some papers, making a few speeches now and then… Eventually, reading, studying, writing… you eventually ask yourself questions: “Really? –I don’t understand this.” Or, “I don’t understand this THIS way. Let’s try it to write it the other way around…” And, maybe, sometimes, this try becomes a paper –most of the times it doesn’t, though.
Either way, the most important thing, I insist, I’ve been doing this because I enjoy it: it’s a challenge to understand someone’s other paper, a new technique, a new subject… It it’s not, if it’s boring, if I’m doing it because “I have to” –and not because it’s fun-, then I just quit: let’s forget this s***.
Turns out that, now and then, some colleagues found some of my papers deserved to be published in some not too bad journals. Great! –This is good for my status and, in time I get some extra pay because of it: not too bad. Others enjoy some of my speeches. Good: you feel good when others like what you’re doing. I have interesting conversations about maths with colleagues here and there and, since I’ve been very lucky, I’ve found funny people around the world to have some laughing and share beers talking about spectral sequences that don’t want to converge when you need them to do it: silly, isn’t it?
Most of the time, though, research is a lonely business: you, your sheet of paper, and your pen.
Do you like it? Do you keep soiling sheets and sheets of papers, from which you’re going to save just 10% -or less? Do you like it, or do you do it because “you have to”?
Well, I couldn’t survive doing it because “I have to”. But because I like it. Because it’s great fun.