This post How do mathematicians conduct research? includes some explanation on things mathematicians do. I am now also a little curious about how much money/resources are used in this process.
For simplicity, let's suppose a pure maths professor gets a research grant of, say, 200 thousand, or 1 million USD. (Over a couple of years.) Note I have edited the amount according to the comments below.
Then, what is the typical list of things on which he or she spends the money, and how much roughly will be spent on each item? 1 million or 100 thousand is a pretty large amount, so the list of things on which we spend the money is probably a bit long, I guess. For example, roughly how much of the grants will be spent on PhD students? (I know the quantity is not fixed. I am just looking for some rough idea.)
I think an answer to this question would be very helpful for understanding how research in pure maths works. (After all, the spending of maths research is going to be very different from a scientist who works in a lab!)
Note that I am specifically asking about pure mathematics (analysis, geometry, number theory, etc, etc). I hope that this will narrow the scope of this question to a sufficient extend for an answer.