All of mathematics is a tale about groups.

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.

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

Geometry is the art of correct reasoning from incorrectly drawn figures.

Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.

Thought is only a flash between two long nights, but this flash is everything.

How is error possible in mathematics?