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Does one have to be an amazing problem solver to become a mathematician or its the passion and dedication? Can every mathematician solve the IMO problems? What is required to solve IMO problems.

tapadia newlon
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Quoted from Terence Tao's career advice (see here): "But mathematical competitions are very different activities from mathematical learning or mathematical research; don’t expect the problems you get in, say, graduate study, to have the same cut-and-dried, neat flavour that an Olympiad problem does. (While individual steps in the solution might be able to be finished off quickly by someone with Olympiad training, the majority of the solution is likely to require instead the much more patient and lengthy process of reading the literature, applying known techniques, trying model problems or special cases, looking for counterexamples, and so forth.)"

Paul
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  • So what does it take to solve IMO problems ,some sort of special training? And can a person who is not so good at such problems still be a successful mathematician – tapadia newlon Feb 02 '15 at 14:09
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    @tapadianewlon Yes and yes (I was never any good at those sort of problems, but I do just fine in research). – Tobias Kildetoft Feb 02 '15 at 14:10
  • Think about this: while trying to solve an IMO problem, you realize a certain formula applies but you need to spend a minute looking it up to remember one or two details. In competition, this could stop you dead in the water. In actual research this is hardly even a speed bump. – David K Feb 02 '15 at 14:13
  • What kind of training should an IMO candidate take – tapadia newlon Feb 02 '15 at 14:15
  • @tapadianewlon A simple counting argument suffices to show that skill with IMO problems is not required for a successful mathematical career. – MJD Feb 02 '15 at 17:04