Science Daily recently reported on a new study  that shows that intellectual curiosity is a good predictor of academic performance. A few days ago I published the post Liberal-Artsy people. Now I know that what I was talking about are people with intellectual curiosity! In the earlier post, I contrasted them with what I called “B.Sc.” types, who are narrowly focused and are not interested in asides in math class about the connections with some concept and other concepts, stories about the discoverer of the concept, the meaning of the name of the concept, and so on.
So better names would be “IC people” instead of Liberal Artsy people and “NF people” (Narrow Focus people) instead of B.Sc. This is better terminology because it isn’t the type of undergraduate degree they have that matters but their attitude toward knowledge of the world.
There are things to say about these concepts with respect to research mathematicians. I have known a good many over the years. (My advice to young people who want to do math research is: Hang around people who know more than you do.) My impression is that most of the very best mathematicians are IC people who are interested in all sorts of things, not just their branch of math.
Even so, some of the best mathematicians are narrowly focused. This has always been the case. Isaac Newton was evidently IC but Kurt Gödel was apparently NF. (He had no interest in things outside math. On the other hand, he did find a new model of general relativity, so he was willing to look at others parts of math besides logic.)
I have known some NF mathematicians. When I wanted to tell them about something they might say, “I have enough trouble keeping up with my field”. The ones that I knew were mediocre and rarely published much beyond writing up their dissertation. I suspect that the famous NF mathematicians were simply brilliant enough to get away with being NF.
Perhaps the sort of NF student whose eyes glaze over when
- you mention Evariste Galois’s tough and short life, or
- talk about how group theory can be used to classify crystals, or
- mention that “tangent” comes from the Latin word for “touching”
are doomed to the same mediocrity. But undoubtedly some of those NF students will turn out to do great things, and some of the IC students will wind up dilettanting through life and never coming close to achieving their potential.
Don’t prejudge students.
 S. von Stumm, B. Hell, T. Chamorro-Premuzic. The Hungry Mind: Intellectual Curiosity Is the Third Pillar of Academic Performance. Perspectives on Psychological Science, 2011; 6 (6): 574 DOI: 10.1177/1745691611421204