In most sciences, there will normally at any given point be a lot of such problems which are too hard for most scientists, but solvable by a few really smart people.

If this picture - rather an elitist one - is right, what are the consequences for policy? It seems to me that the most obvious consequence is that we need to make sure that the most talented people's time is spent in a rational way. Firstly, it does not seem to me that they should spend time teaching students - their time is far too valuable for that. Overall, it's a bit strange that researchers are expected to teach since they really are two quite different jobs.

Let me offer an alternate conclusion. We don't have enough talented scientists to go around. Therefore, our highest priority should be inspiring and training more top-notch scientists. And that means that when somebody is known to be good, we should (A) put them in front of a room to inspire young people, and (B) have them work closely with junior scientists so that the younger scientists can see how very talented people think about problems.

There's a number of scientists who have had a whole string of phenomenally successful graduate students. In physics for instance, John Wheeler had a string of excellent students (including Feynman, Thorne, and Unruh.) Likewise, Dennis Sciama advised Hawking, Rees, David Deutsch, and more. In computer science, people like David Patterson and John McCarthy have had similar influence.

We don't really know how to teach or create scientific brilliance, and so the best we have is to take promising junior people, have them work as assistants to somebody really good, and hope that they pick up some of the habits and thought patterns that worked for their advisor.

Let me put down some evidence, instead of just-so-stories. Different countries do this differently. Europe, more than the United States, goes in for research institutes with paid professional staff and no students. The Max Plank Institutes, INRIA, and so forth, are a much bigger part of the European scientific system than the national laboratories are in the US. We, instead, have much more funding directed to academic faculty who combine their research with undergraduate teaching and graduate advising. My sense is that the US model is at least as effective, and maybe more so. It certainly is not a serious handicap to American science.