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Pure logic could never lead us to anything but tautologies it can create nothing new not from it alone can any science issue.
Henri Poincare
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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
Astronomer
Engineer
Mathematician
Philosopher
Philosopher Of Science
Physicist
Researcher
Topologist
University Teacher
Le Cateau
Jules Henri Poincaré
Poincaré
Henri Poincare
Jules Henri Poincare
Poincare
Issues
Create
Alone
Tautology
Science
Logic
Anything
Issue
Nothing
Scientist
Never
Lead
Pure
More quotes by Henri Poincare
Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
Henri Poincare
Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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Zero is the number of objects that satisfy a condition that is never satisfied. But as never means in no case, I do not see that any progress has been made.
Henri Poincare
But for harmony beautiful to contemplate, science would not be worth following.
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.
Henri Poincare
...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
Henri Poincare
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.
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.
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 and not a precise idea on which reasoning could take hold.
Henri Poincare
Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Henri Poincare
In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.
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.
Henri Poincare
Every good mathematician should also be a good chess player and vice versa.
Henri Poincare
Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.
Henri Poincare
Intuition is more important to discovery than logic.
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? Man, then, can not be happy through science but today he can much less be happy without it.
Henri Poincare
All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.
Henri Poincare
Mathematical discoveries, small or great are never born of spontaneous generation.
Henri Poincare
I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry.
Henri Poincare
Mathematics is the art of giving the same name to different things.
Henri Poincare