Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

A mathematics teacher is a midwife to ideas.

Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.

If you cannot solve the proposed problem try to solve first some related problem.

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