Henri Poincaré

It is by logic that we prove, but by intuition that we discover.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.

Mathematics is the art of giving the same name to different things.

How is it that mathematicians find the truth and we do not? They are not free, they are prisoners of logic.

The mind uses a thousand observations to create a new truth.

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.

The mathematical thermic is the study of the laws of heat, but it is also the study of the most beautiful problems in mathematics.

It is the glory of geometry to be able to advance with sure steps without knowing where it will lead.

One geometry cannot be more true than another; it can only be more convenient.

The future belongs to those who believe in the beauty of their dreams.

In the old days, people believed in the stars; today, we believe in science, but both are forms of faith.

Chance favors only the prepared mind.

The function of science is to inquire into the causes of things.

We must learn to live with uncertainty, for absolute certainty is the enemy of discovery.

Geometry is the noblest of sciences because it is the most certain.

The mind is not a vessel to be filled, but a fire to be kindled.

In mathematics, as in life, the important thing is not to solve problems, but to pose them correctly.

The history of science teaches us that the most fertile discoveries are born of error.

To be a poet is to have a soul so quick to discern that no shade of quality escapes it.