What is the point in pure maths?

Many parts of applied maths originated in pure maths. I don't know how much you know about calculus but I can't even begin to describe how useful it is in applied maths. The idea was developed through concepts in pure maths.

This, I was going to mention calculus, but you've saved me the typing

I wouldn't actually use the example of calculus as an example of an application of "pure" maths. For one thing it's extremely old, I think modern examples are more convincing and relevant. For another thing I don't think you can really call it "pure maths".

I don't think Newton had in his mind at all the abstract concept of a function (did anybody at all in Newton's times? I doubt it), but instead conceived of calculus as a matter of motion in physical space. Back in Newton's days, what we today call "pure maths" didn't exist. Mathematics was more or less entirely mathematical physics, the closest thing to a pure mathematician being Fermat.

"Pure maths" in the way that it is usually meant today, didn't really start until around 1800. When it just exploded into life.

Yeah, I understand this now, I posted this without reading the whole thread, so didn't realise it wasn't really pure maths. (I didn't realise that the core syllabus at A level wasn't actually pure maths)

I think that's probably true of most branches of maths.

Without knowing the details I could drop a few names: Random Matrices, Riemann Zeta Function, Quantum Mechanics.

Such a fail troll, you define pure maths as having no real world applications, and then you ask whether pure maths has any real world applications...

It has no practical application, why can't people who work (professionally I mean) in pure maths do something that actually benefits people.
Yes, I know that it helps to explain things like science which have practical application, but we don't need pure maths to help with that once the problem (or whatever it is) is found because people can work out the maths needed without worrying about the silly things like mathematical proof.
Just to clarify my stance, I think if something has real-world application, I no longer consider it to be 'pure maths'. So please don't say things like 'it is useful for solving problems in physics to do with black holes (or whatever)' because then it would no longer be pure maths.
Other than for 'fun', what is the point in pure maths?
EDIT:
Okay, to clarify further. I think 'pure maths' is when people try to prove things that, for all intents and purposes, are self-evidently true. It is impossible to prove something without making assumptions, so mathematical proof is no more valid than scientific proof just because it makes different assumptions. Also, when people work on problems with numbers or algebra (or whatever) that they can't clearly see an application for (an application being something that would benefit other people). Just because applications are often found later, that doesn't justify finding out the methods used earlier on, because those same methods could have been discovered when the real-life problem arose.

You strongly imply that you don't think that Maths has any real world applications and thus is pointless- well this will obviously be the case when you yourself define pure maths as having no real-world practical application.

I was asking what the point of it is if it can't be applied to real-life.

I am not at all sure that the pure/applied distinction is useful. It's just an old pedagogical term (I took an A-level called 'Applied Mathematics') that should be allowed to die.

Mathematics can be studied to different levels of depth, extent and rigour. If you study it on its own then you are studying mathematics. If you are using mathematics to model real world phenomena then you are doing Physics/Biology/Computer Science etc.

We should be doing Statistics.