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Freeman Dyson has famously characterized two styles of mathematics, that of the bird and that of the frog. I was asked recently the following question, which I don't know how to answer: If, in graduate school, you were raised by frogs, how do you go about becoming a bird? (I'm sure the opposite question is also interesting.)

I feel like the question is really tough to answer, because what one "cuts one's teeth on" in graduate school so deeply biases you to a certain kind of question. My (tinny sounding) attempt at an answer was that one should simply look for problems one is attracted to and has the tools to try to solve. The person, I think, was more interested in knowing what the fundamental difference in "taste" and "style" is between the research sensibility of the bird and that of the frog....and how to move toward one style after having been trained in another...

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I can’t really imagine worrying about it. One does what one enjoys and works on the problems that catch one’s interest. (It’s the sort of question that makes me realize how very different people can be!) –  Brian M. Scott Nov 15 '12 at 17:02
@Brian: I agree. Just get tenure first! –  Jon Bannon Nov 15 '12 at 17:20
I think you are what you are, if you are bird being mentored by the frogs, it is not unusual to spread your wings after grad school (probably little hard). If you have enough deep knowledge about a subject (or an area) you can always modify your working style. –  DBS Jul 9 '13 at 6:44

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