About Mathematicians (Unsourced)

"A mathematician does Mathematics because he sees in it something beautiful, something interesting, something he likes, something to be fond of, something that affects him, something that makes him think, meditate, dream." (Grigore C Moisil)

"A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem." (Jean Dieudonné)

"All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They’re adults in the crystalline world, infants in the real one." (Sylvain Cappell)

"Empirical evidence can never establish mathematical existence—nor can the mathematician's demand for existence be dismissed by the physicist as useless rigor. Only a mathematical existence proof can ensure that the mathematical description of a physical phenomenon is meaningful." (Richard Courant)

"Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies." (Stefan Banach)

"Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness." (Eric T Bell)

"I do believe in simplicity. It is astonishing as well as sad, how many trivial affairs even the wisest thinks he must attend to in a day; how singular an affair he thinks he must omit. When the mathematician would solve a difficult problem, he first frees the equation of all encumbrances, and reduces it to its simplest terms. So simplify the problem of life, distinguish the necessary and the real. Probe the earth to see where your main roots run." (Henry David Thoreau)

"In my opinion a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy - an opinion, moreover, which has been expressed by many philosophers." (Henri Lebesgue)

"In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life." (Michael Atiyah, "The Art of Mathematics" [in "Art in the Life of Mathematicians"])

"Mathematicians have never been in full agreement on their science, though it is said to be the science of self-evident verities - absolute, indisputable and definitive. They have always been in controversy over the developing aspects of mathematics, and they have always considered their own age to be a period of crisis." (Henri Lebesgue)

"Mathematicians do not study objects, but relations between objects. Thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only." (Henri Poincaré)

"Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth." (Marston Morse)

"Mathematics is the life supreme. The life of the gods is mathematics. All divine messengers are mathematicians. Pure mathematics is religion. Its attainment requires a theophany." (Friederich von Hardenberg [Novalis])

"More than any other science, mathematics develops through a sequence of consecutive abstractions. A desire to avoid mistakes forces mathematicians to find and isolate the essence of problems and the entities considered. Carried to an extreme, this procedure justifies the well-known joke that a mathematician is a scientist who knows neither what he is talking about nor whether whatever he is talking about exists or not." (Élie Cartan) 

"Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does." (Louis J Mordell [quoted by Howard Eves, "Mathematical Circles Adieu", 1977])

"No mathematician nowadays sets any store on the discovery of isolated theorems, except as affording hints of an unsuspected new sphere of thought, like meteorites detached from some undiscovered planetary orb of speculation." (James J Sylvester)

"On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols’ […]. Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient." (Jean Dieudonné)

"So if you could be the Devil and offer a mathematician to sell his soul for the proof of one theorem - what theorem would most mathematicians ask for?" (H Montgomery)

"The mathematical method is the essence of mathematics. He who fully comprehends the method is a mathematician." (Friederich von Hardenberg [Novalis])

"The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God." (John W N Sullivan)

"The mathematician's best work is art […] a high and perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch each other." (Gustav Mittag-Leffler)

"The mathematician’s eye is a mystic mirror, not only reflecting reality but absorbing it." (Francis O Googol)

"[…] the mathematician learns early to accept no fact, to believe no statement, however apparently reasonable or obvious or trivial, until it has been proved, rigorously and totally by a series of steps proceeding from universally accepted first principles." (Alfred Adler)

"The real mathematician is an enthusiast per se. Without enthusiasm no mathematics." (Friederich von Hardenberg [Novalis])

"The science of physics does not only give us [mathematicians] an oportunity to solve problems, but helps us also to discover the means of solving them, and it does this in two ways: it leads us to anticipate the solution and suggests suitable lines of argument." (Henri Poincaré)

"There is an intimate and powerful conviction among mathematicians, that supports them in their abstract researches, namely that none of their problems cannot remain without an answer." (Gheorghe Ţiţeica)

"What makes a great mathematician? A feel for form, a strong sense of what is important. Möbius had both in abundance. He knew that topology was important. He knew that symmetry is a fundamental and powerful mathematical principle. The judgment of posterity is clear: Möbius was right." (Ian Stewart)