Applied mathematics is funded because of its practical use. Pure mathematics, like other theoretical fields, is funded to explore ideas practically oriented people ignore. Most of the time such exploration produces nothing of practical value. But occasionally theoreticians stumble upon ideas that turn out to be fundamental to understanding something practically oriented people discover much later.

> It's funded because of its practical use.

That's exactly what the Simons foundation was set up to reject, and it's one of most important funding streams for math

Mathematics as a field will not cease to exist, and not everyone will be interested in (or qualified to) managing the fields progress and its applications.

Haha, the breaks from reality there are two, one professionals do not spend most of their time inventing proofs, and two, practical use? :-)