In pure mathematics, as in many other walks of life, we tend to hail the work of a small minority

(Old question: the figures who prove fundamental theorems that reduce whole tranches How much of earlier work to mere corollaries, or who invent mathematics is or revolutionise could be done by the techniques 'geniuses'?)

A lot of a whole field, important theorems or who are simply so prolific and wide-ranging that it seems almost every paper on anything ought even theories end up being named after or otherwise attributed to cite themone person or a small group of people. It seems to be generally This is often fair, but taken as read an overall trend it can give the (hopefully false!) impression that without such people, the most important mathematics would stagnateis being done by a small minority of mathematicians. 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 does the top $n$ most highly-regarded mathematicians of their generationopposite phenomenon occur, where we currently have about $10n$ career mathematicians per generation. These people are guaranteed jobs it's very clear that let them have as much time as they like for research, while everyone else a result is persuaded to take up another career, or to specialise in teaching. How much slower would progress on a large team effort and that no small group of authors deserves the big problems be if onlylion's share of the very best were doing researchcredit? Let's say they The most obvious example I can also recruit graduate students for menial work, but they have no professional collaborators outside think of is the elite.

There's probably no clear answer hereClassification of Finite Simple Groups, but it'd be interesting to see people's viewsI'm sure there are others from different areas of maths.How much is research in your area dominated by a few big names, and how much do they need us mortals?

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?