It is through science that we prove, but through intuition that we discover.Collection: Science
Mathematics is the art of giving the same name to different things.Collection: Art
One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.Collection: Science
The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.Collection: Knowledge
If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.Collection: Nature
Science is built up of 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.Collection: Science
To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.
It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.
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.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance.
Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.
If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment.
A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.
If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws.
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.Collection: Math
It is with logic that one proves; it is with intuition that one invents.Collection: Intuition
Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.Collection: Believe
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.Collection: Science
There are no solved problems; there are only problems that are more or less solved.Collection: Knowledge
Geometry is the art of correct reasoning from incorrectly drawn figures.Collection: Art
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.Collection: Teaching
Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.Collection: Truth
Intuition is more important to discovery than logic.Collection: Discovery
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.Collection: Party
Guessing before proving! Need I remind you that it is so that all important discoveries have been made?Collection: Science