Quotations by George Pólya
The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face a blackboard and to turn his back on the class. He writes a, he says b, he means c, but it should be d.
Geometry is the science of correct reasoning on incorrect figures.
My method to overcome a difficulty is to go round it.
If there is a problem you can't solve, then there is an easier problem you can't solve: find it.
All the above are from How to Solve It (Princeton 1945).
Mathematics consists of proving the most obvious thing in the least obvious way. Quoted in N Rose Mathematical Maxims and Minims (Raleigh N C 1988).