140 Quotes by Henri Poincare

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

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

"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."

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

"All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance."

"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 and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain."

"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."

"All of mathematics is a tale about groups."

"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."

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