It's a fair question mostly because of how effective math has been at solving practical problems, but honestly working on problems like these is usually due to

It's a fair question mostly because of how effective math has been at solving practical problems, but honestly working on problems like these is usually due to a genuine appreciation and enjoyment of mathematics. I'd even say the majority of mathematicians study math strictly out of a sense of wonder and curiosity rather than towards a commercial application and that the vast majority of math research is not at all practical. The cost is justified due to a common shared interest in the subject, many other people are interested in math and pay people to work on it. It's not all that different than paying someone for music, or a painting, or to write a work of fiction. People get a profound sense of enjoyment and happiness from this work and are happy to pay the cost for the continued advancement of this field.