“Mathematicians may flatter themselves that they possess new ideas which mere human language is yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations of their minds.”

— James Clerk Maxwell

"Thomson & Tait's Natural Philosophy" in Nature, Vol. 7 (Mar. 27, 1873) A review of Elements of Natural Philosophy https://archive.org/details/elementsnatural00kelvgoog (1873) by Sir W. Thomson, P. G. Tait. See Nature, Vol. 7-8, https://archive.org/details/nature7818721873lock Nov. 1872-Oct. 1873, pp. 399-400, or The Scientific Papers of James Clerk Maxwell, p. 328. https://books.google.com/books?id=lzlRAAAAYAAJ&pg=PA328

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

Help us to complete the source, original and additional information

Do you have more details about the quote "Mathematicians may flatter themselves that they possess new ideas which mere human language is yet unable to express. L…" by James Clerk Maxwell?

James Clerk Maxwell 27

Scottish physicist 1831–1879

Related quotes

“We can now return to the distinction between language and symbolism. A symbol is language and yet not language. A mathematical or logical or any other kind of symbol is invented to serve a purpose purely scientific; it is supposed to have no emotional expressiveness whatever. But when once a particular symbolism has been taken into use and mastered, it reacquires the emotional expressiveness of language proper. Every mathematician knows this. At the same time, the emotions which mathematicians find expressed in their symbols are not emotions in general, they are the peculiar emotions belonging to mathematical thinking.”

R. G. Collingwood (1889–1943) British historian and philosopher

Source: The Principles of Art (1938), p. 268

“Ebbinghaus: Language is a system of conventional signs that can be voluntarily produced at any time.
Croce: Language is articulated, limited sound organized for the purpose of expression.
Dittrich: Language is the totality of expressive abilities of individual human beings and animals capable of being understood by at least one other individual.
Eisler: Language is any expression of experiences by a creature with a soul.
B. Erdmann: Language is not a kind of communication of ideas but a kind of thinking: stated or formulated thinking. Language is a tool, and in fact a tool or organ of thinking that is unique to us as human beings.
Forbes: Language is an ordered sequence of words by which a speaker expresses his thoughts with the intention of making them known to a hearer.
J. Harris : Words are the symbols of ideas both general and particular: of the general, primarily, essentially and immediately; of the particular, only secondarily, accidentally and mediately.
Hegel: Language is the act of theoretical intelligence in its true sense, for it is its outward expression.
Jespersen: Language is human activity which has the aim of communicating ideas and emotions.
Jodl: Verbal language is the ability of man to fashion, by means of combined tones and sounds based on a limited numbers of elements, the total stock of his perceptions and conceptions in this natural tone material in such a way that this psychological process is clear and comprehensible to others to its least detail.
Kainz : Language is a structure of signs, with the help of which the representation of ideas and facts may be effected, so that things that are not present, even things that are completely imperceptible to the senses, may be represented.
De Laguna: Speech is the great medium through which human co-operation is brought about.
Marty: Language is any intentional utterance of sounds as a sign of a psychic state.
Pillsbury-Meader: Language is a means or instrument for the communication of thought, including ideas and emotions.
De Saussure: Language is a system of signs expressive of ideas.
Schuchardt. The essence of language lies in communication.
Sapir: Language is a purely human and non-instinctive method of communicating ideas, emotions and desires by means of a system of voluntarily produced symbols.”

Géza Révész (1878–1955) Hungarian psychologist and musicologist

Footnote at pp. 126-127; As cited in: Adam Schaff (1962). Introduction to semantics, p. 313-314
The Origins and Prehistory of Language, 1956

“If our titles recall the known myths of antiquity, we have used them again because they are the eternal symbols upon which we must fall back to express basic psychological ideas....(they) express something real and existing in ourselves.”

Mark Rothko (1903–1970) American painter

radio broadcast, together with Adolph Gottlieb, 1943
1940's

“If you are possessed by an idea, you find it expressed everywhere, you even smell it.”

Thomas Mann book Tonio Kröger

Variant translation: It is strange. If an idea gains control of you, you will find it expressed everywhere, you will actually smell it in the wind.
As translated by Bayard Quincy Morgan
Tonio Kröger (1903)

“But how can we avoid the use of human language? The… symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.”

Tobias Dantzig (1884–1956) American mathematician

p, 125
Number: The Language of Science (1930)

“The genius of democracies is seen not only in the great number of new words introduced but even more in the new ideas they express.”

Alexis De Tocqueville book Democracy in America

Book One, Chapter XVI.
Democracy in America, Volume II (1840), Book One

“Ouspensky records a conversation in St. Petersburg during the summer of 1916 in which Gurdjieff discussed the problem of communication, and the impossibility of conveying in our ordinary language ideas which are intelligible and obvious only for a higher state of consciousness. Speaking of the unity between man, the Universe, and God, he said that the objective knowledge by which alone this unity is to be understood can never be expressed in words or logical forms. At this point, Gurdjieff made a statement which is a key to the understanding of his own subsequent writings. He said:

Realising the imperfection and weakness of ordinary language, the people who have possessed objective knowledge have tried to express the idea of unity in ‘myths,’ in ‘symbols,’ and in particular ‘verbal formulas,’ which, having been transmitted without alteration, have carried on the idea from one school to another, often from one epoch to another.

In All and Everything Gurdjieff makes extensive use of these three forms, that is, symbol, myth, and verbal formula….”

John G. Bennett (1897–1974) British mathematician and author

Gurdjieff’s All and Everything (1950)

“The picture of the 'New Flower' ['Het Bloempje', 1880] is really one of those I did with much idea of having to express loveliness and youth both in human feeling and in the naturally plants of flowers, and If I may say don't you find, that I have succeed in this composition?”

Jozef Israëls (1824–1911) Dutch painter

Quote from his letter, 23 March 1906, to F.W. Gusaulus in Toledo, (TMA); as cited in Jozef Israëls, 1824 – 1911, ed. Dieuwertje Dekkers; Waanders, Zwolle 1999, p. 306
This remark Israëls wrote 26 years after finishing the watercolor; probably it was a gift to the American art-critic
Quotes of Jozef Israels, after 1900

“The making of a journalist: no ideas and the ability to express them.”

Karl Kraus (1874–1936) Czech playwright and publicist

Half-Truths and One-And-A-Half Truths (1976)

“[A]ll our symbols have the same purpose; words are merely the symbols we use most commonly. The function of words in human thought is to stand for things which are not present to the senses, and allow the mind to manipulate them—things, concepts, ideas, everything that does not have a physical reality in front of us now.”

Jacob Bronowski (1908–1974) Polish-born British mathematician

"The Imaginative Mind in Art" (1978)

Help us to complete the source, original and additional information

James Clerk Maxwell 27

Related quotes

Related topics