Jacques S Hadamard - Collected Quotes

"It is important for him who wants to discover not to confine himself to one chapter of science, but to keep in touch with various others." (Jacques S Hadamard, "An Essay on the Psychology of Invention in the Mathematical Field", 1945)

"Practical application is found by not looking for it, and one can say that the whole progress of civilization rests on that principle." (Jacques S Hadamard, "An Essay on the Psychology of Invention in the Mathematical Field", 1945)

"The rules of algebra show that the square of any number, whether positive or negative, is a positive number: therefore, to speak of the square root of a negative number is mere absurdity. Now, Cardan deliberately commits that absurdity and begins to calculate on such 'imaginary' quantities. 

One would describe this as pure madness; and yet the whole development of algebra and analysis would have been impossible without that fundament - which, of course, was, in the nineteenth century, established on solid and rigorous bases. It has been written that the shortest and best way between two truths of the real domain often passes through the imaginary one." (Jacque S Hadamard, "An Essay on the Psychology of Invention in the Mathematical Field", 1945)

"When I undertake some geometrical research, I have generally a mental view of the diagram itself, though generally an inadequate or incomplete one, in spite of which it affords the necessary synthesis - a tendency which, it would appear, results from a training which goes back to my very earliest childhood." (Jacques S Hadamard, "The Psychology of Invention in the Mathematical Field", 1945)

"The creation of a word or a notation for a class of ideas may be, and often is, a scientific fact of very great importance, because it means connecting these ideas together in our subsequent thought" (Jacques S Hadamard, "Newton and the Infinitesimal Calculus", 1947)

"Develop a honeybee mind, gathering ideas everywhere and associating them fully." (Jacques S Hadamard, "But You Don't Understand the Problem", Electronic News, 1967)

"Logic merely sanctions the conquests of the intuition." (Jacques S Hadamard)

"The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there never was any other object for it." (Jacques S Hadamard)