If mathematicians were only occupied with the currently applicable problems, they would not be as productive as one may think, and it may even stunt overall development.

As Alan Turing has shown, aside from a proof itself, it is impossible to know what the proof of a given problem is - or even if one exists! And that's supposing we even know what the problem is!

Taking the example of Fermat's Last Theorem, many people have spent their lives trying to solve it. When Andrew Wiles discovered a proof, it relied on eliptical curves - which is quite disconnected from the problem. Granted this isn't exactly an applicable solution, but it does demonstrate the point that if it weren't for other mathematicians doing maths unguided by applications, then the result would not be possible.

Although Pure Maths may often appear wasteful of time and efforts, it is key to the advancement of technology.

So lets make sure there's funding for it!