Why do universities fund Ph.D. students in the sciences? I was recently accepted into an applied math Ph.D. here in the U.S., and being the 1st in my family to graduate from university, I had a hard time explaining to them why my university will be spending close to 50k on me per year (stipend, tuition, health insurance, fees).

I know that I will be working for the university as a TA, and that perhaps that will go towards covering some of the costs outlined previously, however, it hardly seems to justify the full expenditure.
A good question. Why would the school make this investment (which could be closer to $100K/year)?


As pointed out, if you are TAing/grading/teaching, you are providing services that the school charges undergraduates for.
The funding of a university is not entirely like that of a business. Some of the money is a direct investment in purely academic pursuits, especially that from grants. Educating people and doing basic research is part of what that money is allocated for.
Averaged over all the graduate students, the direct value that they provide to the university in terms of research which goes on to get grants/prestige/donations/patents is substantial.
There is a non-trivial chance that you will become a wealthy donor to the school.