“In every department of physical science there is only so much science, properly so-called, as there is mathematics.”

Man desires concord; but nature know better what is good for his species; she desires discord.

From the crooked timber of humanity, a straight board cannot be hewn.

Happiness is not an ideal of reason, but of imagination.

Never wish to see a just cause defended with unjust means.

A great part, perhaps the greatest part, of the business of our reason consists in the analysation of the conceptions which we already possess of objects.

How then is perfection to be sought? Wherein lies our hope? In education, and in nothing else.

By a lie a man throws away, and as it were, annihilates his dignity as a man.

The hand is the visible part of the brain.

Have the courage to use your own reason- That is the motto of enlightenment.

What can I know? What ought I to do? What can I hope?

Dignity is a value that creates irreplaceability.

Give me matter, and I will construct a world out of it!

Enlightenment is man’s emergence from his self-imposed immaturity. Immaturity is the inability to use one’s understanding without guidance from another.

The history of nature, begins with good, for it is God’s work; the history of freedom begins with badness, for it is man’s work.

Nothing is divine but what is agreeable to reason.

If the truth shall kill them, let them die.

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.

The essence of mathematics lies precisely in its freedom.

In mathematics the art of proposing a question must be held of higher value than solving it.

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.

Maths is totally done differently to what I was teached when I was at school.

In mathematics we have long since drawn the rein, and given over a hopeless race.

Eternity is said not to be an extension of time but an absence of time, and sometimes it seemed to me that her abandonment touched that strange mathematical point of endlessness, a point with no width, occupying no space.