Does all mathematical formulas and proofs have a real world application?

Question

although I only have a minor expertise myself, I've always been fascinated by great thinkers (mostly in the mathematical and technical sciences) and I was wondering if you could help me answer a question. I've just watched the movie "The man who knew infinity" about Srinivasa Ramanujan. In this (and movies like it) are a lot various and (to me) strange formulas mentioned.

I was wondering if all mathematical proofs and formulas have a real world application or if some formulas are only for the fun of it? In my limited knowledge I for example don't understand what practical uses there would be for the p(n) formula (also called an integer partition, which is a way of writing n as a sum of positive integers). Would something like this help us shoot rockets to outer space? understand black holes or something else entirely?

Answer 1

Jacobi said:

It is true that Fourier had the opinion that the principal aim of mathematics was public utility and explanation of natural phenomena; but a philosopher like him should have known that the sole end of science is the honor of the human mind, and that under this title a question about numbers is worth as much as a question about the system of the world.

Source: http://www-history.mcs.st-and.ac.uk/Quotations/Jacobi.html