I hope everyone knows about competitive programming. There are so many sites where you can solve programming tasks and increase your rating. I am curious, does site about something like this for math exist? The service, where we can solve different math tasks and compete with each other. P.S. I know, it's pretty hard to implement autocheck system for math tasks' solutions unlike in competitive programming.
Maybe Project Euler? Mostly those problems are not solved by pure programming.
There are such things for students — specifically (typically) high-school (i.e., pre-collegiate) students. (I don’t know whether age limits are applied.) Perhaps the best known one is the International Mathematical Olympiad, which is held annually (home page, Wikipedia). If you search for “math olympiad”, you’ll find others, mostly for even younger students and/or for smaller competition areas (e.g., state or country).
Khan Academy is adding more college undergraduate-level math topics. It's not competitive in the same way that TopCoder or Project Euler are in the programming world, but it certainly is gamified like StackExchange is (points and badges). For the type of math that is taught to engineers, it's not hard to get a computer to evaluate answers. Evaluating proofs is another story.