So mathematicians can justify their employment.

Theres actually a fascinating conversation about how much of math is real vs how much is imaginary and how long math is just theoretical until an application finds it. But teaching math is only a small part of what math professors do; alot of it is spent further developing the field, and that requires new developments to get or keep the teaching job. And thats been the system for a long time. Courts in the medieval period would sponsor mathematicians, but there was only so much money which could be allocated for that, so mathematicians would challenge each other to see who could do math the best. If you know how to solve a problem no one else does, you have alot better chance at getting that job.