“After Riemann had made known his discoveries, mathematicians busied themselves with working out his system of geometrical ideas formally; chief among these were Christoffel, Ricci, and Levi-Civita. Riemann… clearly left the real development of his ideas in the hands of some subsequent scientist whose genius as a physicist could rise to equal flights with his own as a mathematician. After a lapse of seventy years this mission has been fulfilled by Einstein.”

— Hermann Weyl

Source: Space—Time—Matter (1952), Ch. 2 "The Metrical Continuum"

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Hermann Weyl 28

German mathematician 1885–1955

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“Scientific discovery consists in the interpretation for our own convenience of a system of existence which has been made with no eye to our convenience at all.
One of the chief duties of a mathematician in acting as an advisor to scientists is to discourage them from expecting too much of mathematicians.”

Norbert Wiener (1894–1964) American mathematician

As quoted in Comic Sections (1993) by D MacHale

“If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?”

David Hilbert (1862–1943) German prominent mathematician

Quoted in Mathematical Mysteries : The Beauty and Magic of Numbers (1999) by Calvin C. Clawson, p. 258

“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

“Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians' observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real. …There may be three dimensions in this room and five next door. As a professional mathematician, I have no idea; I can only ask some competent physicist to instruct me in the facts.
The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. …Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers.”

G. H. Hardy (1877–1947) British mathematician

"The Theory of Numbers," Nature (Sep 16, 1922) Vol. 110 https://books.google.com/books?id=1bMzAQAAMAAJ p. 381

“A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.”

Henri Poincaré (1854–1912) French mathematician, physicist, engineer, and philosopher of science

"Notice sur Halphen," Journal de l'École Polytechnique (Paris, 1890), 60ème cahier, p. 143. See also Tobias Dantzig, Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954) p. 8
Context: A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.... we work not only to obtain the positive results which, according to the profane, constitute our one and only affection, as to experience this esthetic emotion and to convey it to others who are capable of experiencing it.

“The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work”

James Whitbread Lee Glaisher (1848–1928) English mathematician and astronomer

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 467 : On the importance of broad training

“Not many years had elapsed after the first edition of this work, when it became known to all with whom Mr. Malthus had the opportunity of communicating on the subject, or who were acquainted with his last publications, that his opinions on the subject of value had undergone some change.”

Thomas Robert Malthus Principles of Political Economy

Advertisement to the Second Edition, p. vii
Principles of Political Economy (Second Edition 1836)

“If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.”

Alfred Tarski (1901–1983) Polish-American logician

Source: The Semantic Conception of Truth (1952), p. 41.

“Every person has his own ideas of the act of praying for God's guidance, tolerance, and mercy to fulfill his duties and responsibilities.”

Walt Disney (1901–1966) American film producer and businessman

Deeds Rather Than Words (1963)
Context: Every person has his own ideas of the act of praying for God's guidance, tolerance, and mercy to fulfill his duties and responsibilities. My own concept of prayer is not as a plea for special favors nor as a quick palliation for wrongs knowingly committed. A prayer, it seems to me, implies a promise as well as a request; at the highest level, prayer not only is a supplication for strength and guidance, but also becomes an affirmation of life and thus a reverent praise of God.

“His obedience is real since he really and truly fulfills his mission, since he runs real risks in order to carry out the beloved’s orders. But, on the other hand, it is imaginary because he submits only to a creature of his mind.”

Jean Paul Sartre book Saint Genet

152
Saint Genet, Actor and Martyr (1952)

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