What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment.

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think

All of mathematics is a tale about groups.

Geometry is not true, it is advantageous.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

Mathematical discoveries, small or great are never born of spontaneous generation.