Can you provide me historical examples of pure mathematics becoming "useful"? I am trying to think/know about something, but I don't know if my base 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 practical application).
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"?

This may be a little late but I think the most basic and pure proof and yet the most astonishing was Euclid's
Wikipedia Entry on Euclid
There are uses in Digital Media, Cryptography, Physics and Engineering.
A lot of Pure math is knowing how to apply it, most theories have a specific problem set they are known to solve because they are designed that way or were found to solve that problem set that way but when you apply theories in ways which are not typical of the solution you incite innovation and expand your horizons.
