Henri Poincare quote

"It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem."

Henri Poincare

Born: April 29, 1854

Die: July 17, 1912

Occupation: Mathematician

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More quotes of Henri Poincare

Henri Poincare

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or,...

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Henri Poincare

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature...

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Henri Poincare

Mathematical discoveries, small or great are never born of spontaneous generation.

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Henri Poincare

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.... The two propositions: "The earth turns round"...

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Henri Poincare

The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would...

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Henri Poincare

Mathematicians are born, not made.

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Henri Poincare

Mathematics is the art of giving the same name to different things. [As opposed to the quotation: Poetry is the art of giving different names to the same thing].

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Henri Poincare

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant:...

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Henri Poincare

Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.

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Henri Poincare

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.

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Henri Poincare

The mind uses its faculty for creativity only when experience forces it to do so.

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Henri Poincare

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means ...

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Henri Poincare

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

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Henri Poincare

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

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Henri Poincare

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think

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Henri Poincare

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

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Henri Poincare

A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

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Henri Poincare

Point set topology is a disease from which the human race will soon recover.

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Henri Poincare

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.

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Henri Poincare

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.

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Henri Poincare

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.

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Henri Poincare

Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.

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Henri Poincare

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...

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Henri Poincare

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...

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Henri Poincare

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

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Henri Poincare

Astronomy is useful because it raises us above ourselves; it is useful because it is grand; .... It shows us how small is man's body, how great his mind, since his intelligence can embrace the whole of...

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Henri Poincare

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

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Henri Poincare

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

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Henri Poincare

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

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Henri Poincare

We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.

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Henri Poincare

It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

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Henri Poincare

A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we say that this effect is due to chance.

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Henri Poincare

Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.

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Henri Poincare

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. They reveal the kinship between other facts,...

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Henri Poincare

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...

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Henri Poincare

Einstein does not remain attached to the classical principles, and when presented with a problem in physics he quickly envisages all of its possibilities. This leads immediately in his mind to the prediction...

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Henri Poincare

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly...

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Henri Poincare

All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As for the calculations themselves, they must be made in...

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Henri Poincare

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

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Henri Poincare

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.

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Henri Poincare

It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.

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Henri Poincare

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

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Henri Poincare

Hypotheses are what we lack the least.

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Henri Poincare

Thought is only a flash between two long nights, but this flash is everything.

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Henri Poincare

Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon...

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Henri Poincare

Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse...

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Henri Poincare

Intuition is more important to discovery than logic.

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Henri Poincare

It is by logic we prove. It is by intuition we discover.

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Henri Poincare

Analyse data just so far as to obtain simplicity and no further.

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Henri Poincare

In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.

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Henri Poincare

It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are...

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Henri Poincare

Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages....

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Henri Poincare

Tolstoi explains somewhere in his writings why, in his opinion, "Science for Science's sake" is an absurd conception. We cannot know all the facts since they are infinite in number. We must make a selection...

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Henri Poincare

I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success,...

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Henri Poincare

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done....

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Henri Poincare

Mathematicians do not study objects, but relations between objects.

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Henri Poincare

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

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Henri Poincare

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

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Henri Poincare

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry...

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Henri Poincare

When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes...

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Henri Poincare

What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic....

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Henri Poincare

Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures.

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Henri Poincare

How is error possible in mathematics?

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Henri Poincare

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

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Henri Poincare

Les faits ne parlent pas. Facts do not speak.

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Henri Poincare

On fait la science avec des faits, comme on fait une maison avec des pierres; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison. Science is built up with...

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Henri Poincare

All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is...

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Henri Poincare

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is...

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Henri Poincare

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

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Henri Poincare

Geometry is not true, it is advantageous.

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Henri Poincare

If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness?...

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Henri Poincare

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

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Henri Poincare

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

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Henri Poincare

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.

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Henri Poincare

So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without;...

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Henri Poincare

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture...

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Henri Poincare

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

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Henri Poincare

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

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Related quote

Henri Poincare

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature...

Read more


Gabriel Lippmann

[On the Gaussian curve, remarked to Poincaré:] Experimentalists think that it is a mathematical theorem while the mathematicians believe it to be an experimental fact.

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George Boole

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.

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Joseph de Maistre

War is thus divine in itself, since it is a law of the world. War is divine through its consequences of a supernatural nature which are as much general as particular. War is divine in the mysterious glory...

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Neil deGrasse Tyson

There is a theorem that colloquially translates, You cannot comb the hair on a bowling ball. ... Clearly, none of these mathematicians had Afros, because to comb an Afro is to pick it straight away from...

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G. H. Hardy

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics,...

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Richard Bach

He spoke of very simple things- that it is right for a gull to fly, that freedom is the very nature of his being, that whatever stands against that freedom must be set aside, be it ritual or superstition...

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J. H. Hexter

If physicists could not quote in the text, they would not feel that much was lost with respect to advancement of knowledge of the natural world. If historians could not quote, they would deem it a disastrous...

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Nicolaus Copernicus

Since, then, there is no objection to the mobility of the Earth, I think it must now be considered whether several motions are appropriate for it, so that it can be regarded as one of the wandering stars....

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Rollo May

We must be fully committed, but we must also be aware at the same time that we might possibly be wrong. People who claim to be absolutely convinced that their stand is the only right one...is a dead giveaway...

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Percy Williams Bridgman

The result is that a generation of physicists is growing up who have never exercised any particular degree of individual initiative, who have had no opportunity to experience its satisfactions or its possibilities,...

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Frederic Bastiat

...the statement, "The purpose of the law is to cause justice to reign," is not a rigorously accurate statement. It ought to be stated that the purpose of the law is to prevent injustice from reigning....

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Soren Kierkegaard

Truth is not something you can appropriate easily and quickly. You certainly cannot sleep or dream yourself to the truth. No, you must be tried, do battle, and suffer if you are to acquire the truth for...

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Jon Stewart

Even if the flag burning amendment does become law, the larger problem will remain of how to respectfully dispose of older, tattered flags. Well, fortunately the U.S. official Flag Code has a suggestion...

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Tertullian

The Law found more than it lost when Christ said, ‘Love your enemies and pray for those who persecute you, so that you may be sons of your Father who is in heaven’ (Matthew 5:44-45). This most important...

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Edwin Hubbel Chapin

Truth is new, as well as old. It has new forms; and where you may find a new statement, an earnest statement, you may conclude that by the law of progress it is more likely to be a correct statement than...

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George Polya

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences,...

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Mark Twain

Evolution is a blind giant who rolls a snowball down a hill. The ball is made of flakes-circumstances. They contribute to the mass without knowing it. They adhere without intention, and without foreseeing...

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Chen-Ning Yang

In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are...

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Paul Davies

The temptation to believe that the Universe is the product of some sort of design, a manifestation of subtle aesthetic and mathematical judgment, is overwhelming. The belief that there is "something behind...

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Ken Cuccinelli

My view is that homosexual acts, not homosexuality, but homosexual acts are wrong. They’re intrinsically wrong. And I think in a natural law based country it’s appropriate to have policies that reflect...

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