“Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.”

— Antoine Augustin Cournot , Researches into the Mathematical Principles of the Theory of Wealth

Source: Researches into the Mathematical Principles of the Theory of Wealth, 1897, p. 3 ; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/198/mode/2up, (1914) p. 33: About the nature of mathematics

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Antoine Augustin Cournot 5

French economist and mathematician 1801–1877

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Context: Between two absolutely different spheres, as between subject and object, there is no causality, no correctness, and no expression; there is, at most, an aesthetic relation: I mean, a suggestive transference, a stammering translation into a completely foreign tongue — for which I there is required, in any case, a freely inventive intermediate sphere and mediating force. "Appearance" is a word that contains many temptations, which is why I avoid it as much as possible. For it is not true that the essence of things "appears" in the empirical world. A painter without hands who wished to express in song the picture before his mind would, by means of this substitution of spheres, still reveal more about the essence of things than does the empirical world. Even the relationship of a nerve stimulus to the generated image is not a necessary one. But when the same image has been generated millions of times and has been handed down for many generations and finally appears on the same occasion every time for all mankind, then it acquires at last the same meaning for men it would have if it were the sole necessary image and if the relationship of the original nerve stimulus to the generated image were a strictly causal one. In the same manner, an eternally repeated dream would certainly be felt and judged to be reality. But the hardening and congealing of a metaphor guarantees absolutely nothing concerning its necessity and exclusive justification.

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Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 287; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/4/mode/2up, (1914), p. 5: Definitions and objects of mathematics.

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“Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.”

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Antoine Augustin Cournot 5

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