Henri Poincare Quotes

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

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.

It is with logic that one proves; it is with intuition that one invents.

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

There are no solved problems; there are only problems that are more or less solved.

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.

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

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

It is far better to foresee even without certainty than not to foresee at all.

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.

Mathematicians are born, not made.

Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.

Intuition is more important to discovery than logic.

It is not order only, but unexpected order, that has value.

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?

Chance ... must be something more than the name we give to our ignorance.

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

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

Often when works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, long or short, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind.

It is through science that we prove, but through intuition that we discover.

A small error in the former will produce an enormous error in the latter.

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?

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

To invent is to discern, to choose.