Are Contest Math and Research Mathematics Really That Different?

[arachnotron]

Hi, all!

I was wondering: is research mathematics (the stuff real professionals do) anything like contest mathematics? I know contest math is usually extremely hard and requires ingenuity, but does mathematics at, say, the graduate level require more mathematical ability/ingenuity than the "toy" problems prevalent in elementary math based contest math?

I'm a math "newbie", so I'm not all too privy to the distinction between contest math and the real world!

(note: when I say "contest math", I mean things like USAMO/IMO, etc. -- the highest level stuff)

 

[glueball8]

Don't know about that but my current math teacher always says "Its not problem solving if you seen the problem before!"

So I'm guess you don't need to be brilliant at math to study it. If you love it then do it...

 

[arachnotron]

Bright Wang,

I'm not sure what you mean?

 

[Vid]

Most of the contest math problems revolve around finding a simple trick using mostly elementary mathematics under time constraints. Graduate students and professional mathematicians have to learn, relearn, and coherently organize large volumes of mathematical theory with hopes of somehow extending, even in some insignificant way, this body of knowledge.

 

[gunch]

Contest math is quite a bit different than research math, but many of the same skills are used. I went to the last IMO and plan to go this time too, but just because it's a great experience and you meet interesting people. I don't expect to use many of the weird factorization techniques I know, but I certainly think that contest math has helped me solve problems, including non-contest and even non-mathematical problems, better. For some good advice see:
http://terrytao.wordpress.com/career-advice/advice-on-mathematics-competitions/

 

[Hurkyl]

My opinion is that being good at contest math isn't enough to have the deep insights to solve hard problems -- but it will mean that you are very good at connecting the dots, and thus at assembling deep insights into useful theorems.

 

[arildno]

As in all research, the MAJOR distinguishing feature of "real math" relative to contest math, is to be able to FORMULATE a solvable, and interesting, problem.

 

[mathwonk]

good point, problem finding, and problem posing, are crucial research skills nit represented in most contests, although there is no reason contests could not become more extended in scope. the purpose of a contest is to engage young people in a fun activity, so the problems are purposely chosen to be challenging but not to be completely discouragingly impossible. In actual research you are up against nature and the problems have no ceiling in difficulty.