Jacques Hadamard Quotes (1865-1963)

“With Klein, even politics has been introduced into the question: he asserts that “It would seem as if a strong naive space intuition were an attribute of the Teutonic race, while the critical, purely logical sense is more developed in the Latin and Hebrew races.” That such an assertion is not in agreement with facts will appear clearly when we come to examples. It is hardly doubtful that, in stating it, Klein implicitly considers intuition, with its mysterious character, as being superior to the prosaic way of logic and is evidently happy to claim that superiority for his countrymen. We have heard recently of that special kind of ethnography with Nazism: we see that there was already something of this kind in 1893.”

“The systematic study of the singularities of analytic functions was begun by Hadamard. In 1901, a very valuable account of his own investigations together with those of other early workers, as Fabry, Leau, LeRoy, Borel and others, was presented by Hadamard in his now classic little book La Série de Taylor et son Prolongement Analytique published in the Collection Scientia (No. 12).”

“... Professor Hadamard concludes that the general pattern of invention, or, as it might also be put, of original work, is three-fold : conscious study, followed by unconscious maturing, which leads in turn to the moment of insight or illumination. Thereupon another period of conscious work ensues, the purpose of which is to achieve a synthesis of several elements: the novel idea, its logically deduced consequences including proof, and the traditional knowledge to which the new item is added. Hadamard's investigation, modest and tentative as are its results, seems to me of capital importance in the realm of criticism and cultural history. For what he has done is to show that the human mind tends to behave much the same way whenever it invents, whether in mathematical or in poetic form—a conclusion which does not deny differences of temperament. Our author, on the contrary, is at pains to distinguish among types of mathematical geniuses. He classes them as logical or intuitive, concrete or abstract, yet with enough flexibility to allow for deceptive appearances and for the overlapping of categories. But it is clear in the end that in any process of creation there lurks a mystery—a mystery at least equal to that of thinking itself.”

“All those who were acquainted with Hadamard know that until the end of his very long life, he retained an extraordinary freshness of mind and character: in many respects, his reactions remained those of a fourteen-year-old boy. His kindness knew no bounds. The warmth with which Hadamard received me in 1921 eliminated all distance between us. He seemed to me more like a peer, infinitely more knowledgeable but hardly any older; he needed no effort at all to make himself accessible to me.”