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I'm trying to think/know about something but I don't know if my basis premise is plausible, here we go.

Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because it has no practical utility, but I guess that according to the history of mathematics, the math that is useful today was once pure mathematics (I'm not so sure but I guess that when the calculus was invented, it hadn't a pratical aplication).

Also, I guess that the development of pure mathematics is important because it allows us to think about non-intuitive objects before encountering some phenomena that is similar to these mathematical non-intuitive objects, with this in mind can you provide me historical examples of pure mathematics becoming "useful"?

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Newton invented his fluxions (i.e. his calculus) in order to compute the orbits of celestial objects that move according to his law of gravitation. The foundations of calculus as pure mathematics were not established until the 18th century. –  Ron Gordon Jan 17 '13 at 5:42
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@JavaMan: I think there might be some debate as to whether string theory is useful ... –  Henry B. Jan 17 '13 at 5:49
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@HenryB or whether an application of pure mathematics to pure mathematics is what the OP had in mind. –  Willie Wong Jan 17 '13 at 8:48
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Two similar posts under the heading "Useless math that became useful" here and on MO. –  Martin Jan 17 '13 at 8:52
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@Brad I think rglordonma was answering the OP's point about calculus being invented without a practical application, which is false as it was invented exactly for a practical application. –  user50229 Jan 17 '13 at 20:02

33 Answers 33

Matrix operations were used by Pauli to model electron spin.

Pauli spin matrix

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Formulas for calculating the value of PI to millions , billions and Trillions of digits seemed to have no practical utility .Testing new Computer technology ,which were millions or billions of times faster than old technologies and had millions of times more memory than old technologies ,required the use of these formulas .

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protected by Zev Chonoles Feb 22 '13 at 8:24

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