On Language (Unsourced)

"Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable." (Alfred N Whitehead)

"I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language." (Werner Heisenberg)

"It will probably be the new mathematical discoveries which are suggested through physics that will always be the most important, for, from the beginning Nature has led the way and established the pattern which mathematics, the Language of Nature, must follow." (George D Birkhoff)

"[...] languages are not really means for representing already known truths, but are rather instruments for discovering previously unrecognised ones." (Wilhelm von Humboldt)

[…] mathematics has liberated itself from language; and one who knows the tremendous labor put into this process and its ever-recurring surprising success, cannot help feeling that mathematics nowadays is more efficient in it particular sphere of the intellectual world than, say, the modern languages in their deplorable condition of decay or even music are on their fronts. (Andreas Speiser)

"Math is the language of the universe. So the more equations you know, the more you can converse with the cosmos." (Neil deGrasse Tyson)

"Mathematics is a way of expressing natural laws, it is the easiest and best way to describe a general law or the flow of a phenomenon, it is the most perfect language in which one can narrate a natural phenomenon." (Gheorghe Ţiţeica)

"Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. [...] It is also an art - the most intellectual and classical of the arts." (Alfred Adler)

"[…] mathematics has liberated itself from language; and one who knows the tremendous labor put into this process and its ever-recurring surprising success, cannot help feeling that mathematics nowadays is more efficient in it particular sphere of the intellectual world than, say the modern languages in their deplorable condition of decay or even music are on their fronts." (Andreas Speiser)

"[…] mathematics is not, never was, and never will be, anything more than a particular kind of language, a sort of shorthand of thought and reasoning. The purpose of it is to cut across the complicated meanderings of long trains of reasoning with a bold rapidity that is unknown to the mediaeval slowness of the syllogisms expressed in our words." (Charles Nordmann)

"Nature responds only to questions posed in mathematical language, because nature is the domain of measure and order." (Alexandre Koyré)

"Such is the advantage of a well-constructed language that its simplified notation often becomes the source of profound theories." (Pierre-Simon Laplace)    

"Symbolism transforms the phenomenon into the idea, and the idea into an image in such a fashion that in the image the idea remains infinitely active and incommensurable, and if all languages were used to express it, it would still remain inexpressible." (Johann Wolfgang von Goethe, "Maxims and Reflections", [posthumous])

"The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics." (Johannes Kepler)

"The laws of Nature are written in the language of mathematics […]" (Galileo Galilei)

The Mathematics will be the Latin language of the future, compulsory for all scientists. Just because the Mathematics allows maximum acceleration of the movement of the scientific ideas. (Grigore C Moisil)

"Time is said to have only one dimension, and space to have three dimensions [...] The mathematical quaternion partakes of both these elements; in technical language it may be said to be ‘time plus space’, or ‘space plus time’: and in this sense it has, or at least involves a reference to, four dimensions.

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." (Eugene Wigner)

"The motive of science was the extension of man, on all sides, into Nature, till his hands should touch the stars, his eyes see through the earth, his ears understand the language of beast and bird, and the sense of the wind; and, through his sympathy, heaven and earth should talk with him. But that is not our science." (Ralph W Emerson)

"The mutual interdependence of thought and word illuminates clearly the truth that languages are not really means for representing already known truths, but are rather instruments for discovering previously unrecognised ones. The differences between languages are not those of sounds and signs but those of differing worldviews […] objective truth always rises from the entire energy of subjective individuality." (Wilhelm von Humboldt)

"The simplicities of natural laws arise through the complexities of the language we use for their expression." (Eugene Wigner) 

"There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction." (Thomas Merton)

"Thought is metaphoric, and proceeds by comparison, and the metaphors of language derive therefrom." (Ivor A Richards)

"We are trapped by language to such a degree that every attempt to formulate insight is a play on words." (Niels Bohr)

"What is the inner secret of mathematical power? Briefly stated, it is that mathematics discloses the skeletal outlines of all closely articulated relational systems. For this purpose mathematics uses the language of pure logic with its score or so of symbolic words, which, in its important forms of expression, enables the mind to comprehend systems of relations otherwise completely beyond its power. These forms are creative discoveries which, once made, remain permanently at our disposal. By means of them the scientific imagination is enabled to penetrate ever more deeply into the rationale of the universe about us." (George D Birkhoff)

"When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system." (John von Neumann)

"Whether man is disposed to yield to nature or to oppose her, he cannot do without a correct understanding of her language." (Jean Rostand)

"You may translate books of science exactly. […] The beauties of poetry cannot be preserved in any language except that in which it was originally written." (Samuel Johnson)