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)?
Universities don't "fund" Ph.D. candidates. They pay them salaries - or what should be recognized as salaries - to do research. In more normal states (such as the Netherlands), nobody is trying to deny this fact, and PhD candidates are formally in a employer-employee legal relation with their university. In other states (such as the US, or rather individual states within the federation) there are on-again-off-again legal struggles regarding this question.
As an example, look for the US NLRB decisions 332-111 (October 31st, 2000, NYU) and later decision 342-42 (July 13 2004, Brown U) edit: and the recent and excellent 364-90 (August 23 2016, Columbia U).
By the way, even employment in teaching isn't always recognized, and occasionally (again, in the US specifically, but less so in recent years) universities try to pass off the teaching work as training/learning experience and not pay PhD candidates for it.
Now, of course it's not quite that simple: The relation of a PhD candidate and his/her university is not entirely the same as that of the line worker and the factory, or the typist and office etc. When you're in a PhD program you are still learning and acquiring skills; however, unlike an undergraduate student, you do this mostly by carrying out actual research work (and perhaps also teaching work). These two types of activity are what a university is supposed carry out, so you are significantly contributing to realizing the university's (ongoing) objectives. A PhD candidate is a trained professional in his general field already when s/he is inducted, and s/he gradually acquires expertise, hones skills, and trains in the research aspect of his/her discipline, as opposed to other applicative aspects of it.
I think another point worth considering is that two of the costs you list this as covering, tuition and fees, go back to the university. So while they might technically be losing money on paper by giving you these things, you could see it more as a form of creative accounting. They are not actually losing it, but rather not making it.
Depending on the university and how they operate, they might expect to regain more of the money you are given in your stipend via other means (housing, food, parking, etc.).
Once you account for the difference between on-paper spending on you and how much you are actually getting in real money, you can start explaining the rest of it as the fact you are in fact doing work for the university. Working as a TA, doing research, and other tasks involved in the Ph.D process.
It's worth considering that Ph.D students are in the same job market as other bachelors / masters holders, and that the university needs to compete with the non-academic market to an extent. Depending on the field, you might be foregoing a substantial salary by obtaining a Ph.D. Not everyone is necessarily going to be willing to do that, so offering a lot of freebies can encourage people who might go straight to business to remain in academia, at least briefly.
As such, it's probably more helpful to view this money as a combination of discounts and payment for TA/research work. Trying to build favor with you should you become a successful researcher no doubt plays a part as well.
I don't think the accepted answer really addresses the question and want to put forward my own opinion. STEM PhDs are funded for a few reasons:
Health care: cancer, Ebola, Zika, etc. are important problems that society agrees need to be solved. At least in the US, the NIH invests heavily in biomedical research, and many fields try to align themselves with this funding, e.g. a computer scientist or mathematician turned computational biologist.
Tech companies: Most major universities now have entrepreneurship-support programs, and no one wants to miss out on the next Google.
Compare this to someone getting their PhD in theology. I am not arguing that their work does not have social value, but I think we can safely say that society at large is not willing to invest as much—if any—money.
Fair or not and right or wrong, I think this is why STEM PhDs are funded: we want the innovative technology that is built on top of basic scientific research.* In lieu of this, I'd argue that PhD students are pretty cheap labor.
* I think an interesting question is why do STEM fields have such immense practical value? Thomas Kuhn and Eugene Wigner both address this topic. My favorite answer is one that I think is fairly parsimonious: Scientific fields are practical because if a field is practical, we call science.
Because you will be a source of incredibly cheap highly skilled labor. This is especially the case if your field involves lab work.
As an example, I was a statistician at a major research institute shortly after graduating. This institute included graduate students. When any of the research cores needed my help, they were (internally) billed $160/hour. Alternatively, the PI's could try to get their graduate students to do the work instead. Of course, there's no direct bill involved in asking a graduate student to do your work, but you do have to fund their $50k a year. If they were to work 40 hours a week, this would amount to $25/hr...except I would guess that most of them averaged 50 hours a week (at least). And then some of the students were funded by outside money, which saved them even more!
So you can see that the institute saved a whole bunch of money by having grad students.
An answer already given is a good one, but an advisor once summarized funding and degrees in a rather pithy way that bears repeating here:
Universities want money from professional degrees, so they hope you go out into the world, become wealthy, and donate to them later, but charge you up front in case you don't
Universities want prestige from research degrees, so they cover your expenses so you don't have to worry about making money and can go out in the world and become famous, but make you do menial labor for next to nothing, in case you don't
For those unfamiliar with the dichotomy:
The other answers nicely address the direct relationship between the university and the graduate student, and why the university might want to fund the graduate studies. While all true, in my opinion, this largely misses the point of STEM graduate students.
At a research university, the STEM stars are the faculty, who bring in a lot of grant money. The primary purpose of graduate students is to provide those faculty with research (and teaching) assistance. Creating a graduate program is considered a benefit for faculty.
If graduate students are paid at below-market rates, then the faculty will not get good students, they will not be happy, and their research (and, more importantly in the eyes of the university, their grant money) will suffer.
If you're starting your applied math graduate studies at the University of Texas at Austin, you may well end up working at the Center for Subsurface Modeling, a research group devoted to the mathematical study of underground fluids. You'll be doing this in a state that gets an enormous amount of revenue from underground fluids, and a state where lawns and cattle and people depend on underground fluids to survive. Many Americans depend on underground fluids, which is why the US National Science Foundation just gave the Center for Subsurface Modeling $1.5 million to keep studying them. Many Ph.D. students worked very hard to help bring in that $1.5 million grant. You will work very hard to help bring in the next one.
In general, universities pay for graduate work in the sciences because they think graduate work in the sciences pays off. Sometimes the payoff is a huge jackpot that everyone notices. Sometimes the payoff is a huge jackpot that few will ever understand. Sometimes the payoff builds up slowly over fifty years and quietly remakes the world. Sometimes the big payoff looks too surreal to be worth hundreds of thousands of dollars of actual money, but there are other little payoffs with more practical benefits. Sometimes the payoff is so deep that it's hard to guess what benefits it might bring.
I don't know why universities and their funding agencies seem to value graduate work in the sciences more than graduate work in the humanities. After all, humanities graduate students also go on to bring down international crime rings, serve on state supreme courts, organize major social movements, and change the way we see the world. Maybe it's because the payoffs of graduate research are less immediate in the humanities: I can't point to any humanities Ph.D. theses that led directly to practical applications, the way I can in the sciences. (Of course, the humanities are far outside my area of expertise.) Maybe it's because the government and industry stakeholders who drive investment in sciences graduate studies are more wary of the returns humanities graduate studies can bring.
Whatever the cause of the funding gap between sciences and humanities, you can at least assure your family that applied math Ph.D.s are widely considered a solid investment. Applied mathematicians often work on pretty practical problems, and they sometimes collaborate directly with industry partners. Your university will be spending 50 grand a year on you because they convinced some funding agencies that your training and research will be worth it, and their industrial affiliates will be laughing all the way to the gas station.
Many universities consider research (as much or even more than teaching) to be their core business. PhD students drive research. They help academics to remain research-productive and before the end of their PhDs, they are productive researchers in their own right. By publishing papers and helping academics to win research funding, they help to draw extra funding into the university and also help to keep the university's research ranking, and hence national and international reputation, high. This in turn helps to increase the numebr and quality of undergraduate students who want to study at the university, which also brings in money. Universities may also receive direct government funding for graduating PhD students.
Because that number of "$50k per year" is imaginary. Anyone they are charging "$50k per year" is essentially paying for your education and being rewarded with a place at the university.
I know others had similar answers/comments, but they were too long and complicated.
