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I am writing an essay for a scholarship and they asked the following question: "How will these goals enable you to help others?"

Although I am majoring in pure math, this really got me to think about the applications of pure math. I know that when Ramanujan discovered the Mock Theta functions, he predicted that they would play a vital role in the future. And decades later, they did! A better example might be of G.H. Hardy, who boasted that his work in Number Theory was useless and not applicable in the real world. Well, we know how that went.

So my question to the community is, do all mathematical ideas eventually find their way into the real world? I realize this is a broad question, but I would love to hear everyone's thoughts on it. I hope questions such as this are allowed on the site!

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    $\begingroup$ Hard to prove "eventually", because it involves predicting the future. $\endgroup$ Commented Feb 3, 2017 at 2:44
  • $\begingroup$ Very hard to say. A lot of math actually just get buried under the sand of time. $\endgroup$ Commented Feb 3, 2017 at 2:47
  • $\begingroup$ @MatthewLeingang Yes, if only we had a time machine! $\endgroup$ Commented Feb 3, 2017 at 2:50
  • $\begingroup$ @JackyChong That's a shame. I wonder how much beautiful math we don't know because of this $\endgroup$ Commented Feb 3, 2017 at 2:52
  • $\begingroup$ Um, well, I like the chipper spirit of this question, but I'm not sure about your examples. I don't know of any applications of mock theta functions or virtually anything that Hardy did outside of mathematics. $\endgroup$ Commented Feb 3, 2017 at 13:50

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Going for a very logical answer, I would say NO, assuming that the world ends someday. The proof is simple, you can create some unuseful math stuff just before the world ends! If you have infinite time, the answer might be different!

Joking aside, I believe math is a branch of art. I look at it just the way I look at Painting, Music, and other arts. Are they in practical use? I do not think so. But they are aesthetically useful. The beauty they provide is their application itself.

But I'm not suggesting saying this to get the scholarship because it will probably not work. You can try to find some way to justify that your work will have some application. Alternatively, you can spend some time without money but with the beauty of math-art.

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    $\begingroup$ I love this answer, as I love the "math is art" point of view, since it really is art, but with the possibility of loads of real-world applications by it's own nature. $\endgroup$
    – lisyarus
    Commented Feb 3, 2017 at 13:59
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    $\begingroup$ @lisyarus MATH is a Transcendental ART. <3 $\endgroup$
    – MR_BD
    Commented Feb 4, 2017 at 9:19
  • $\begingroup$ Great answer! I totally agree on the math is art part. I wrote that I view math is a language, the language of nature. I know it's a cliche, but it's a much deserved one! I would like to help others learn it. :) $\endgroup$ Commented Feb 4, 2017 at 19:32
  • $\begingroup$ @CuriousMathStudent Me too. Good luck with that... $\endgroup$
    – MR_BD
    Commented Feb 4, 2017 at 20:44
  • $\begingroup$ Your answer very badly misrepresents mathematics. The fact that you can read the posts on Math SE relies on HTTPS, which in turn relies on some elementary number theory, such as via Fermat's little theorem. Given the 100% empirical success of HTTPS, it would be ridiculous to claim that the mathematics behind it is useless. $\endgroup$
    – user21820
    Commented Oct 14, 2018 at 7:08
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A "proof" for @Leila's answer- $No$ :

Topic: Negatives

Leonhard Euler himself could not explain:

if I have 2 things and I take 3, how many things do I have left ?

Source: enter image description here

OF COURSE: Chinese people use negatives ~200BC (recording debts) following the video ealier.

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