About Mathematicians (1940-1949)

"A mathematician, like a painter or a poet, is a maker of patterns. [...]. The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." (Godfrey H Hardy, “A Mathematician's Apology”, 1940)

"At the present time it is of course quite customary for physicists to trespass on chemical ground, for mathematicians to do excellent work in physics, and for physicists to develop new mathematical procedures […] Trespassing is one of the most successful techniques in science." (Wolfgang Köhler, "Dynamics in Psychology", 1940)

"It is a melancholic experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done [...] there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.“  (Godfrey H Hardy, "A Mathematician's Apology“, 1940)

“Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)

“The mathematician is still regarded as the hermit who knows little of the ways of life outside his cell, who spends his time compounding incredible and incomprehensible theorems in a strange, clipped, unintelligible jargon.” (James R Newman, “Mathematics and the Imagination”, 1940)

"[…] there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, [...] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as 'real', but [...] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics." (Godfrey H Hardy, "A Mathematician's Apology", 1940)

"We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for […] The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for." (Hermann Weyl, "The Mathematical Way of Thinking", 1940)

"A serious threat to the very life of science is implied in the assertion that mathematics is nothing but a system of conclusions drawn from definitions and postulates that must be consistent but otherwise may be created by the free will of the mathematician. If this description were accurate, mathematics could not attract any intelligent person. It would be a game with definitions, rules and syllogisms, without motivation or goal." (Richard Courant & Herbert Robbins, "What Is Mathematics?", 1941)

"Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist. He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and observation of the universe." (Edwin P Hubble, "The Problem of the Expanding Universe", 1941)

"Mathematicians themselves set up standards of generality and elegance in their exposition which are a bar to understand." (Kenneth E Boulding, "Economic Analysis", 1941)

"It is to be hoped that in the future more and more theoretical physicists will command a deep knowledge of mathematical principles; and also that mathematicians will no longer limit themselves so exclusively to the aesthetic development of mathematical abstractions." (George D Birkhoff, "Mathematical Nature of Physical Theories" American Scientific Vol. 31 (4), 1943)

"A mathematician is not a man who can readily manipulate figures; often he cannot. He is not even a man who can readily perform the transformations of equations by the use of calculus. He is primarily an individual who is skilled in the use of symbolic logic on a high plane, and especially he is a man of intuitive judgment in the choice of the manipulative processes he employs." (Vannevar Bush, "As We May Think", 1945)

"In various ways, methods of approaching the mathematician's ideal were sought, and the resulting suggestions were the source of much that was mistaken in metaphysics and theory of knowledge.” (Bertrand Russell, “A History of Western Philosophy”, 1945)

"One of the difficulties which a mathematician has in describing his work to non-mathematicians is that the present day language of mathematics has become so esoteric that a well educated layman, or even a group of scientists, can comprehend essentially nothing of the discourse which mathematicians hold with each other, or of the accounts of their latest researches which are published in their professional journals." (Angus E Taylor, "Some Aspects of Mathematical Research", American Scientist , Vol. 35, No. 2, 1947)

"[…] mathematicians progress only by doubt, through humble and constant attempts to impinge on the immense domain of the unknown." (Leopold Infeld, "Whom the Gods Love: The Story of Évariste Galois", 1948)