Math problems that are impossible to solve I recently read about the impossibility of trisecting an angle using compass and straight edge and its fascinating to see such a deceptively easy problem that is impossible to solve. I was wondering if there are more such problems like these which have been proven to be impossible to solve.

One problem which I like is the Bridge of Konigsberg problem.

The challenge is to find a path that crosses each bridge exactly once. 
It was eventually proved to be impossible by Euler and is considered one of the early applications of graph theory.
http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg
