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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?

user361608
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    I think this question got the community a little on edge. First off, it sounds like you are trying to discredit or play off mathematicians' work as opposed to find their motives for curiosity. I do think you deserve an answer though: no, most things that upper level mathematicians study or work on are not directly applicable problems. They are usually branching out into very foreign territories of knowledge and trying to lay the foundation for others to understand and use it. There are plenty of things which are discovered "for fun" and found to be utterly crucial hundreds of years later. – Connor James Aug 16 '16 at 00:02
  • I'm in no way trying to discredit what these great thinkers are able to do, and I'm sorry if my question comes across as such. That was not my intention. – user361608 Aug 16 '16 at 00:11
  • A lot of purely mathematical results later find applications in very surprising ways. And you rarely know, which result will prove crucial and when. Mathematics is great because of its timeless nature - something discovered and written right now could be dusted off and used 200 or 300 years later – Yuriy S Aug 16 '16 at 00:12
  • Cryptography is a great example. It's used by billions of devices daily and relies entirely on discoveries in number theory that weren't usable in the century they were discovered. The newest and most secure form of cryptography today (Elliptic Curve Cryptography) relies on Algebraic Geometry which combined old techniques with niche new-wave math fields to boost its effectiveness. – Connor James Aug 16 '16 at 00:19
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    What's 'real world application' even supposed to mean? Are mathematicians from some other dimension? Are they fictional? – Yuriy S Aug 16 '16 at 00:34
  • I don't think Newton's Method of Convergence was able to be fully utilized until the modern era. With computers, we can get very accurate and quick approximations for a wide variety of numbers like: showing irrational roots on a calculator, solving for location coordinates to track position with GPS, turning abstract mathematical concepts into visible numbers, etc. I always think Newton's Method goes hand in hand with Taylor Series Expansion for, again, making math models produce the numbers we care about in its application. – Connor James Aug 16 '16 at 00:38
  • Cool question about math. – Sigma6RPU Aug 16 '16 at 00:48
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    I just wonder why so many downvotes on this particular question. – Sigma6RPU Aug 16 '16 at 00:51
  • @Yuriy S: Apart from cryptography, do you know examples of pure maths which found an application only 200 or 300 years later? – paf Aug 16 '16 at 00:55
  • @paf We have a question about that and it's got some good answers: http://math.stackexchange.com/questions/486855/what-are-some-examples-of-mathematics-that-had-unintended-useful-applications-mu – Milo Brandt Aug 16 '16 at 01:22
  • Thank you for this very interesting link. – paf Aug 16 '16 at 10:00

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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

paf
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