“I shall here present the view that numbers, even whole numbers, are words, parts of speech, and that mathematics is their grammar.”

— Carl Eckart

Numbers were therefore invented by people in the same sense that language, both written and spoken, was invented. Grammar is also an invention. Words and numbers have no existence separate from the people who use them. Knowledge of mathematics is transmitted from one generation to another, and it changes in the same slow way that language changes. Continuity is provided by the process of oral or written transmission.
Source: Our Modern Idol: Mathematical Science (1984), p. 95.

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Carl Eckart9

American physicist 1902–1973

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“I shall here present the view that numbers, even whole numbers, are words, parts of speech, and that mathematics is their grammar. Numbers were therefore invented by people in the same sense that language, both written and spoken, was invented. Grammar is also an invention. Words and numbers have no existence separate from the people who use them. Knowledge of mathematics is transmitted from one generation to another, and it changes in the same slow way that language changes. Continuity is provided by the process of oral or written transmission.”

Carl Eckart (1902–1973) American physicist

Source: Our Modern Idol: Mathematical Science (1984), p. 95.

“It is true that in recent years a number of attractive histories of mathematics have been published in England and America, but these have only dealt with Greek mathematics as part of the larger subject, and in consequence the writers have been precluded… from presenting the work of the Greeks in suflicient detail. The same remark applies to the German histories of mathematics, even to the great work of Moritz Cantor…”

Thomas Little Heath (1861–1940) British civil servant and academic

Preface p. vi
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

“I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

Grundlagen einer allgemeinen Mannigfaltigkeitslehre [Foundations of a General Theory of Aggregates] (1883)

“Arithmetic and geometry, according to Plato, are the two wings of the mathematician. The object indeed of all mathematical questions, is to determine the ratios of numbers, or of magnitudes; and it may even be said, to continue the comparison of the ancient philosopher, that arithmetic is the mathematician's right wing; for it is an incontestable truth, that geometrical determinations would, for the most part, present nothing satisfactory to the mind, if the ratios thus determined could not be reduced to numerical ratios. This justifies the common practice, which we shall here follow, of beginning with arithmetic.”

Jacques Ozanam (1640–1718) French mathematician

Source: Recreations in Mathematics and Natural Philosophy, (1803), p. 2

“As Gauss first pointed out, the problem of cyclotomy, or division of the circle into a number of equal parts, depends in a very remarkable way upon arithmetical considerations. We have here the earliest and simplest example of those relations of the theory of numbers to transcendental analysis, and even to pure geometry, which so often unexpectedly present themselves, and which, at first sight, are so mysterious.”

George Ballard Mathews (1861–1922) British mathematician

Part 1, sect. 167.
Theory of Numbers, 1892

“It is not of the essence of mathematics to be conversant with the ideas of number and quantity.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: Alexander Bain (1870) Logic, p. 191

“The whole perspectives in which companies are viewed needs to shift from short to the long-term, and as I would say, to a focus on shapes, not just numbers.”

Indra Nooyi (1955) Indian-born, naturalized American, business executive

CEOs need to change: Indra Nooyi

“Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single fact took the scientific world by storm.”

Douglas Adams Life, the Universe and Everything

Source: Life, the Universe and Everything

“I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe.
Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.”

Marcus du Sautoy (1965) British professor of mathematics

In "Life lessons" http://www.theguardian.com/science/2005/apr/07/science.highereducation?fb_ref=desktop The Guardian (7 April 2005)

“I shall call Ideological State Apparatuses (ISAs) a certain number of realities which present themselves to the immediate observer in the form of distinct and specialized institutions: …”

Louis Althusser book Lenin and Philosophy and Other Essays

the religious ISA (the system of the different churches),
the educational ISA (the system of the different public and private ‘schools’),
the family ISA,
the legal ISA,
the political ISA (the political system, including the different parties),
the trade-union ISA,
the communications ISA (press, radio and television, etc.),
the cultural ISA (literature, the arts, sports, etc.).
Source: Lenin and Philosophy and Other Essays (1968), "Ideology and Ideological State Apparatuses", p. 96

“I shall here present the view that numbers, even whole numbers, are words, parts of speech, and that mathematics is their grammar.”

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Carl Eckart9

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