Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.

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

An idea which can be used only once is a trick. If one can use it more than once it becomes a method.

Mathematics consists in proving the most obvious thing in the least obvious way.

Geometry is the science of correct reasoning on incorrect figures.

In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.