Henri Poincare
Henri Poincare
Jules Henri Poincaréwas a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist by Eric Temple Bell, since he excelled in all fields of the discipline as it existed during his lifetime...
NationalityFrench
ProfessionMathematician
Date of Birth29 April 1854
CountryFrance
means necessary neither nor
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means . . . .
party mean passion
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.
zero mean numbers
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.
mean perfect too-late
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 hampered in their general grasp by third and fourth decimal places.
mean pigs piano
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, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
american-journalist governed phenomenon succeeding
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.
avoiding consists infinite invention useful useless
Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. To invent is to discern, to choose.
american-journalist cannot cause determines due effect escapes notice
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.
american-journalist believe both convenient equally necessity
To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.
american-journalist species
It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
american-journalist relations remain replace
Thus, they are free to replace some objects by others so long as the relations remain unchanged.
american-journalist
No more than these machines need the mathematician know what he does.
wish different looks
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.
effort difficulty
But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.