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"Project Euler exists to encourage, challenge, and develop the skills and enjoyment of anyone with an interest in the fascinating world of mathematics."

From the about page:

How did Project Euler all start?

Project Euler was started by Colin Hughes (a.k.a. euler) in October 2001 as a sub-section on mathschallenge.net. Who could have known how popular these types of problems would turn out to be? Since then the membership has continued to grow and Project Euler moved to its own domain in 2006.

Who runs Project Euler?

Ideas for new problems come from our own members and they are developed by a team of hard working and talented mathematicians and programmers. So to put it simply, it is the members that run Project Euler.