> I think the best and most beautiful mathematics is driven directly by applications, and made better for the pressure to apply to a real problem (not a problem

> I think the best and most beautiful mathematics is driven directly by applications, and made better for the pressure to apply to a real problem (not a problem that just mathematicians care about). That's the thing, in my opinion, when you study math, you start with applications, you work your way to solve complex applicative problems, and then, those problems start to be less interesting, in part because they become easy for you, and the other part is that most of the problem is just 'mechanical and technical' work. Not really interesting. But what you like in math, it's not the maths themselves, it's to be challenged by problems. So you start to work on abstracts problems, until they become easy, then you go one more step in the abstraction, to find challenging problems, etc.. So basically, I find it somewhat natural to be driven always to more abstract theory, with maybe the hope that one day they will be applied. It's far from you to solve too 'technical' problems in the sense that 'it's just an application of XYZ problem to solve, now, I don't want to implement it, as it will take me a lot of time, while I can find pleasure again in discovering new hard things' I'm also on the applicative side, but I understand the attraction of the abstract side, and sometimes, I allow myself to work with just a bit of higher abstraction. So with enough luck, some day, a mathematician, with the right level of abstraction at that moment, will discover an applicative problem that is of your interest, and dedicate to it some time, maybe a lot of time, and maybe even, his/her whole carreer, making it more abstract, elegant and practical.