In pure mathematics, as in many other walks of life, we tend to hail the work of a small minority: the figures who prove fundamental theorems that reduce whole tranches of earlier work to mere corollaries, or who invent or revolutionise the techniques of a whole field, or who are simply so prolific and wide-ranging that it seems almost every paper on anything ought to cite them. It seems to be generally taken as read that without such people, mathematics would stagnate.

What I'm wondering is, how much is the contribution of everyone else? Consider the following thought experiment: someone devises a machine that will reliably predict, let's say just after completing their doctorate, who would eventually earn a place among the top $n$ most highly-regarded mathematicians of their generation, where we currently have about $10n$ career mathematicians per generation. These people are guaranteed jobs that let them have as much time as they like for research, while everyone else is persuaded to take up another career, or to specialise in teaching. How much slower would progress on the big problems be if only the very best were doing research? Let's say they can also recruit graduate students for menial work, but they have no professional collaborators outside the elite.

There's probably no clear answer here, but it'd be interesting to see people's views. How much is research in your area dominated by a few big names, and how much do they need us mortals?

(Old question: How much of mathematics is or could be done by the 'geniuses'?)

A lot of important theorems or even theories end up being named after or otherwise attributed to one person or a small group of people. This is often fair, but taken as an overall trend it can give the (hopefully false!) impression that the most important mathematics is being done by a small minority of mathematicians. What I'm wondering is, how much does the opposite phenomenon occur, where it's very clear that a result is a large team effort and that no small group of authors deserves the lion's share of the credit? The most obvious example I can think of is the Classification of Finite Simple Groups, but I'm sure there are others from different areas of maths.