What we know is not much. What we do not know is immense.

(Allegedly his last words.)

[His last words, according to De Morgan:]

Man follows only phantoms.

Nature laughs at the difficulties of integration.

Read Euler: he is our master in everything.

Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.

Napoleon: You have written this huge book on the system of the world without once mentioning the author of the universe.

Laplace: Sire, I had no need of that hypothesis.

Later when told by Napoleon about the incident, Lagrange commented: Ah, but that is a fine hypothesis. It explains so many things.

[said about Napier's logarithms:]

...by shortening the labours doubled the life of the astronomer.

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematicall speculations.

The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which ofttimes they are unable to account.

It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge.

All the effects of Nature are only the mathematical consequences of a small number of immutable laws.