TITLE: What are the math challenges websites?
QUESTION [17 upvotes]: I know two websites that offer some challening puzzles for programming, Project Euler (PE has something about math, but I feel it's more about programming) and Code-Golf.
Can you recommend me some sites that have the same purpose for maths? Until now I know only The Art of Problem Solving. You can recommend me these websites in any level.

REPLY [3 votes]: A List of Blogs (mostly high level Mathematics). Note that these will not be problem solving for fun kind of sites, rather focus on cutting-edge research problems or problems that involve a lot of dedicated theoretical background. I am posting this list because you have specifically mentioned "any level" in your question.
The List:

Problem Solver's Paradise
Blog on Inequalities - Contains several inequalities related problems
Annoying Precision - A blog with more focus on simplifying explanations on various mathematical topics
Combinatorics related
Godel's Letter and P = NP (Blog Focused on Complexity Theory, Quantum Computation and Formal Logic)
Math less traveled
Area777 - Mostly Topology related

Note that because I am a new user, I can only post 2 links per post. So I'll add the rest in the comments. If my rep increases, I'll come back and edit it.
EDIT: Combined my other post with this one as I now have the rep to post in a single answer :)