cty_therapy). These were brought on by discussions with 
deire on professorial encouragement and discouragement, and with masteralida on the idea of taking students under one's wing.Throughtout these threads, I have been thinking about virtuosity, to wit: how important are natural skill, talent, fluency and style?
- In technical fields such as software development, do they transfer across programming languages?
- In creative subjects such as mathematical theorem proving, does the skill really persist (like the oft-cited one of riding a bicycle) or does it burn out by age 35 in many cases, as the Chronicle of Higher Education postulated about a year and a half ago?
- Hypothetically speaking, is success in some "highly refined and rarefied" circles of math/CS research really constrained more by talent than hard work? Are students who beat themselves against the wall perseverant or in need of a reality check cf. American Idol, or is it the faculty member who pours a bucket of cold water on the aspiring and diligent student really the deluded one?
For what they're worth, here are my personal thoughts:
- Skill is as skill does: that is, skills transfer across fields when they reflect genuine aptitude. A case in point: my father is a chemical engineering virtuoso and a jack-of-all-trades in chemistry.1 But he's always been only competent or good at organic chemistry and biochemistry, and very good at inorganic and analytical chemistry. To really shine, he had to find his way through three iterations of physical chemistry, four graduate universities, a job, and a decade of grad school. Moral: don't give up doing what you love, but also don't give up looking for what you are best at. Or, as the late Prof. Dr. Edsger W. Dijkstra wrote: do only what only you can do.
- Virtuosity is overrated: Here, I have to disagree with Randy Jackson (who frequently asserts on American Idol that the contest is all about natural talent), or at least assert that at least in my field, virtuous practitioners and researchers are born and made, not born rather than made. As an example, I will use myself. I got scores around 90% on calculus exams in high school. As an undergrad, I got scores in the high 90s (even a couple of 100% scores, the only one in the class) on discrete math and combinatorics exams. I wasn't the best at the university, but I was best in the (small) class that year. I will state categorically that despite my ability being imperceptibly diminished since then, I am practially unrecognized as a discrete mathematician. Is it because I haven't published in this area? No, though it isn't my main area2; see my dissertation and the journal papers since. Nothing earth-shattering as combinatorics goes, but the mathematical content is there. Instead, I found something I was actually good at: spotting and addressing methdological gaps and needed syntheses of intelligent systems theory and practice. It's all about perception: your own, that of your colleagues and other peers, even that of your students.
- Teachers who quell ambition in the diligent and motivated are already doing a disservice to young minds: I will go out on a limb and just go ahead and say this. I'm not getting soft in my old age, it has nothing to do with saturation of the field, and it's not because I've been lucky enough to get only talented students. Those who have stayed are talented; I've had to screen many students and, yes, tell some they weren't suited certain research careers in the field. But as jereeza, the right kind of (art) teacher IMO, says: you don't teach by weeding; you don't protect the field from "dilution" by weeding; you reinforce strength where you find it, identify and correct weaknesses, and cautiously, carefully encourage talent. I have seen my share of both heartbreaking lack of confidence and insufferable arrogance that were brought on by bad discipline from an early age, as it were. Let us all resolve - every man Jack and woman Jill of us in educational disciplines - to avert the day when we have to say: I've created a monster. Monster.com is easy to come by; the Gojira emergency response team for overinflated egos - not so much.
Opinions? Comments?
1 As some of you know, chemical engineering, being about process planning, plant design, and applied mathematics and computational science and engineering, is a completely different field from chemistry, which deals with the theory and methodologies for analysis of reactions and substances. These are at least as different as computer science and computing.
2 My main area is more aptly described as applied probability, statistical computation, and even theoretical CS than combinatorics and graph theory.
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