"If some great mathematicians have known how to give lyrical expression to their enthusiasm for the beauty of their science, nobody has suggested examining it as if it were the object of an art - mathematical art - and consequently the subject of a theory of aesthetics, the aesthetics of mathematics." (François Le Lionnais, "Great Currents of Mathematical Thought", 1971)
"Mathematicians are there to find the constraints and to eliminate those things that aren't constraints [...]" (Robert E Machol, Mathematicians are useful, 1971)
"Any mathematician endowed with a modicum of intellectual honesty will recognise then that in each of his proofs he is capable of giving a meaning to the symbols he uses." (René Thom, "Modern mathematics, does it exist?", 1972)
"In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. Chess sometimes plays a similar role. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics." (Stanislaw M Ulam, "Adventures of a Mathematician", 1976)
"You cannot read mathematics superficially; the inescapable abstraction always has an element of self-torture in it, and the one to whom this self-torture is joy is the mathematician." (Rózsa Péter, "Playing with Infinity: Mathematical Explorations and Excursions", 1976)
"Mathematicians do not agree among themselves whether mathematics is invented or discovered, whether such a thing as mathematical reality exists or is illusory." (Albert L Hammond, "Mathematics - Our invisible culture", 1978)
"On the face of it there should be no disagreement about mathematical proof. Everybody looks enviously at the alleged unanimity of mathematicians; but in fact there is a considerable amount of controversy in mathematics. Pure mathematicians disown the proofs of applied mathematicians, while logicians in turn disavow those of pure mathematicians. Logicists disdain the proofs of formalists and some intuitionists dismiss with contempt the proofs of logicists and formalists." (Imre Lakatos,"Mathematics, Science and Epistemology" Vol. 2, 1978)
"A proof is a construction that can be looked over, reviewed, verified by a rational agent. We often say that a proof must be perspicuous or capable of being checked by hand. It is an exhibition, a derivation of the conclusion, and it needs nothing outside itself to be convincing. The mathematician surveys the proof in its entirety and thereby comes to know the conclusion." (Thomas Tymoczko," The Four Color Problems", Journal of Philosophy , Vol. 76, 1979)
"Mathematicians do not agree among themselves whether mathematics is invented or discovered, whether such a thing as mathematical reality exists or is illusory." (Albert L Hammond, "Mathematics - Our invisible culture", 1978)
"On the face of it there should be no disagreement about mathematical proof. Everybody looks enviously at the alleged unanimity of mathematicians; but in fact there is a considerable amount of controversy in mathematics. Pure mathematicians disown the proofs of applied mathematicians, while logicians in turn disavow those of pure mathematicians. Logicists disdain the proofs of formalists and some intuitionists dismiss with contempt the proofs of logicists and formalists." (Imre Lakatos,"Mathematics, Science and Epistemology" Vol. 2, 1978)
"A proof is a construction that can be looked over, reviewed, verified by a rational agent. We often say that a proof must be perspicuous or capable of being checked by hand. It is an exhibition, a derivation of the conclusion, and it needs nothing outside itself to be convincing. The mathematician surveys the proof in its entirety and thereby comes to know the conclusion." (Thomas Tymoczko," The Four Color Problems", Journal of Philosophy , Vol. 76, 1979)
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