“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

Source: Dynamics in Psychology, 1940, p. 116

Adopted from Wikiquote. Last update June 3, 2021. History

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Wolfgang Köhler 12

German-American psychologist and phenomenologist 1887–1967

Aleksandr Zinovyev (1922–2006) Russian writer

On the Social State of Marxism (1978)

“Anyone who compares the bibliography with the reprinted papers will notice that mathematics and physics have not been given equal treatment. There is a strong bias in favor of mathematics. The bias arises from the fact that mathematical papers, provided that are correct and not trivial, have permanent value, whereas most papers in physics journals are ephemeral. For this reason, it is customary to publish complete collected works of mathematicians but only selected works of physicists.”

Freeman Dyson (1923) theoretical physicist and mathematician

Selected Papers of Freeman Dyson with Commentary. https://books.google.com/books?id=nnyNUidX1OMC&pg=PA1 American Mathematical Soc. (1996) p. 1

“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 (1888–1972) German American mathematician (1888-1972)

Richard Courant in: The Parsimonious Universe, Stefan Hildebrandt & Anthony Tromba, Springer-Verlag, 1996, page 148

“So intimate is the union between Mathematics and Physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create for each successive class phenomena a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature. Sometimes the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armory of the mathematician the weapons which he needed ready made to his hand. But much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.”

Henry John Stephen Smith (1826–1883) mathematician

As quoted in The Century: A Popular Quarterly (1874) ed. Richard Watson Gilder, Vol. 7, pp. 508-509, https://books.google.com/books?id=ceYGAQAAIAAJ&pg=PA508 "Relations of Mathematics to Physics". Earlier quote without citation in Nature, Volume 8 (1873), page 450.
Also quoted partially in Michael Grossman and Robert Katz, Calculus http://babel.hathitrust.org/cgi/mb?a=listis;c=216746186|Non-Newtonian (1972) p. iv. ISBN 0912938013.

“If people persist in trespassing upon the grizzlies' territory, we must accept the fact that the grizzlies, from time to time, will harvest a few trespassers.”

Edward Abbey (1927–1989) American author and essayist

“Literature is no one’s private ground, literature is common ground; let us trespass freely and fearlessly and find our own way for ourselves.”

Virginia Woolf (1882–1941) English writer

“…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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

“... like most physicists, I really enjoy talking about physics.”

Nima Arkani-Hamed (1972) American-Canadian physicist

[A Conversation with Nima Arkani-Hamed: The Power of Principles, Physics Revealed (Part I), April 2, 2021, Ideas Roadshow, YouTube, https://www.youtube.com/watch?v=h6_iJRY6nU4] (quote at 2:47 of 57:39)

“Purely mathematical symbols have no meaning by themselves; it is the privilege of pure mathematicians, to quote Bertrand Russell, not to know what they are talking about. …It is the physicist, and not the mathematician, who must know what he is talking about.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932)

“I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.”

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

Source: Ramanujan (1940), Ch. I : The Indian mathematician Ramanujan.

“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.”

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Wolfgang Köhler 12

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