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

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

Every good mathematician should also be a good chess player and vice versa.

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

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

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

Mathematicians do not study objects, but the relations between objects.