Geometry is the science of correct reasoning on incorrect figures.

A GREAT discovery solves a great problem but there is a grain of discovery in any problem.

There are many questions which fools can ask that wise men cannot answer.

When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.

Euclid 's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument.