Is Contest-Math Worth It? I am very interested in Contest-based mathematics. The questions such as the ones that come up in the AMC, or AIME, USAMO and most specifically Putnam are very interesting. 
It is very different however from textbooks like Rudin's Analysis or Number Theory texts for example. 
Would you say the problems justify a true genius? 
 A: There are some factors to consider here:


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*It depends on the type of genius we're talking about (a.k.a. People acing these tests are most likely not geniuses in any other field to the extent they are in math).

*People who get amazing ranks in these competitions, have both skill and luck combo working for them. If one repeatedly wins these kind of competitions, then they are most likely amazing 'Problem-Solvers'.

*'A True Genius' in Mathematics is also very subjective; not only do we have to narrow down to the field they are comfortable with, we have to see in what perspective they excel in that field (Bird or Frog, Theory builders or Problem solvers, etc).

*One thing's for certain: not winning/ being successful in these competitions does in no way mean you are not a genius in Mathematics. 

*To recap, success in these competitions indicate potential, but failure in these exams does not indicate failure in Mathematics and its fields itself.


Interest and big success in Contest-Math certainly indicates a high level of competency and ingenuity in Mathematics, but is not the only deciding factor in determining the level of 'genius' one is. Usually, those who are geniuses, will get a breakthrough some way or the other; either in the aspect of publishing a ground breaking paper, or by solving the most complex of problems, or even by bringing existing conundrums and results into new light.
I'm sure others will put their answers more succinctly, and have better anecdotes to put in their answers; I'm not very experienced with life and Math (Young compared others in this community). So I'm just offering my opinion since it's a soft-question. Hope it offers some insight.
