A clash of doctrine is not a disaster, it is an opportunity.

The art of progress is to preserve order amid change, and to preserve change amid order. Life refuses to be embalmed alive. The more prolonged the halt in some unrelieved system of order, the greater the crash of the dead society.

Education with inert ideas is not only useless; it is above all things harmful.

Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.

To be an abstraction does not mean that an entity is nothing. It merely means that its existence is only a factor of a more concrete element of nature.

You think the world is what it looks like in fine weather at noon day; I think it is what it seems like in the early morning when one first wakes from deep sleep.

The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilised of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.