But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

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.

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

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living