This might be a very stupid question but comes to mind when we encounter each and every topic of pure maths. Why we are studying this, what are the applications of this etc etc. The topics in the pure maths are abstract unlike applied mathematics. What will be the best answer satisfy a student of mathematics, to the question application of mathematics? Actually our mathematics teachers generally dont focus on applications in mathematics. Does this mean that mathematicians are more interested in the extension/generalization of previously known field or results rather than their applications?
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"?
In .NET, what's the best way to prevent multiple instances of an app from running at the same time? And if there's no "best" technique, what are some of the caveats to consider with each solution?