On Language (1900-1919)

"A knowledge of statistics is like a knowledge of foreign languages or of algebra; it may prove of use at any time under any circumstances." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of the great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write." (Herbert G Wells, "Mankind in the Making", 1903)

"The diagram-language into which a proposition in mathematics is translated cannot possibly consist in nothing but a diagram, since no diagram, even if it be a changing one can present more than a single object, while the verbal expression of the proposition to be proved is necessarily general. To revert to our example, a proposition about any spherical triangle whatsoever, relates to something that no single image of a spherical triangle can cover. Accordingly, every diagram must be supplemented by certain general understandings or explicit rules, which shall warrant the substitution for one diagram of any other conforming to certain rules. These will be rules of permissible substitution, partly limited to the special proposition, partly extending to an entire class of diagrams to which this one belongs." (Charles S Peirce, [manuscript] 1903)

"The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of the great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write." (Herbert G Wells, "Mankind in the Making", 1903)

"So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality." (Henri Poincaré, "The Value of Science", 1905)

"Mathematicians, however, are well aware that it is childish to try to show by drawing curves that every continuous function has a derivative. Though differentiable functions are the simplest and the easiest to deal with, they are exceptional. Using geometrical language, curves that have no tangents are the rule, and regular curves, such as the circle, are interesting but quite special." (Jean-Baptiste Perrin, 1906)

"The laws of nature are drawn from experience, but to express them one needs a special language: for, ordinary language is too poor and too vague to express relations so subtle, so rich, so precise. Here then is the first reason why a physicist cannot dispense with mathematics: it provides him with the one language he can speak […]. Who has taught us the true analogies, the profound analogies which the eyes do not see, but which reason can divine? It is the mathematical mind, which scorns content and clings to pure form." (Henri Poincare, "The Value of Science​", 1905)

"Without this language [mathematics] most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world, which is the only true objective reality." (Henri Poincaré," The Value of Science", Popular Science Monthly, 1906)

"The motive for the study of mathematics is insight into the nature of the universe. Stars and strata, heat and electricity, the laws and processes of becoming and being, incorporate mathematical truths. If language imitates the voice of the Creator, revealing His heart, mathematics discloses His intellect, repeating the story of how things came into being. And the value of mathematics, appealing as it does to our energy and to our honor, to our desire to know the truth and thereby to live as of right in the household of God, is that it establishes us in larger and larger certainties. As literature 62 develops emotion, understanding, and sympathy, so mathematics develops observation, imagination, and reason." (William E Chancellor,"A Theory of Motives, Ideals and Values in Education" 1907)

"[…] one does not know a foreign language unless on is able to think in that language; one does not know mathematics unless one is able to think mathematically." (John A L Waddell, 1908)

"Mathematics is the language of definiteness, the necessary vocabulary of those who know. Hence the intimate connection between mathematics and science." (William F White,"A Scrap-book of Elementary Mathematics", 1908)

"The beautiful has its place in mathematics as elsewhere. The prose of ordinary intercourse and of business correspondence might be held to be the most practical use to which language is put, but we should be poor indeed without the literature of imagination. Mathematics too has its triumphs of the Creative imagination, its beautiful theorems, its proofs and processes whose perfection of form has made them classic. He must be a 'practical' man who can see no poetry in mathematics." (Wiliam F White, "A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays", 1908)

Things and events explain themselves, and the business of thought is to brush aside the verbal and conceptual impediments which prevent them from doing so. Start with the notion that it is you who explain the Object, and not the Object that explains itself, and you are bound to end in explaining it away. It ceases to exist, its place being taken by a parcel of concepts, a string of symbols, a form of words, and you find yourself contemplating, not the thing, but your theory of the thing. (Lawrence P Jacks, "The Usurpation Of Language", 1910)

"Language is a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others. (Ferdinand de Saussure, "Course in general linguistics", 1915)