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"?

Group theory is commonplace in quantum mechanics to represent families of operators that possess particular symmetries.  You can find some info here.
