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After i read Gowers's paper on The "Two Cultures of Mathematics" my impression is that a combinatorialist is considered a problem solver.

I am more interested in pure aspects of mathematical analysis, what an analyst is considered in this categorization? a problem solver? a theory builder? or somewhere in between?

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I think analysis has more than enough room for both approaches (and everything in between). –  Gerry Myerson Feb 4 '13 at 9:02
This is kind of silly question! Wouldn't you consider analysts in differential equations or mathematical physicists to be problem solvers? And wouldn't you consider Richard Stanley to be theory builder? It's not that cut and dried. –  Mathemagician1234 Feb 4 '13 at 9:04
As already pointed out, this is not a function of the field, but rather of the person doing it. –  mrf Feb 4 '13 at 9:05
@Mathemagician1234 what a ridiculous way to make a point :) –  Akram Hassan Feb 4 '13 at 9:29

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