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.

It's impossible to define mathematics in a way that satisfies all mathematicians. 
This is likely not the answer you're after, but it stroke me when I first  heard of it because definitions in mathematics are both exact and omnipresent, and I was not suspecting that providing a universal definition of mathematics itself could be such an intractable problem.
