“As professor in the Polytechnic School [autumn of 1858] in Zurich I found myself for the first time obliged to lecture upon the elements of the differential calculus and felt, more keenly than ever before, the lack of a really scientific foundation for arithmetic. In discussing the notion of the approach of a variable magnitude to a fixed limiting value, and especially in proving the theorem that every magnitude which grows continually, but not beyond all limits, must certainly approach a limiting value, I had recourse to geometric evidences. Even now such resort to geometric intuition in a first presentation of the differential calculus, I regard as exceedingly useful, from the didactic standpoint, and indeed indispensable, if one does not wish to lose too much time. But that this form of introduction into the differential calculus can make no claim to being scientific, no one will deny. For myself this feeling of dissatisfaction was so overpowering that I made the fixed resolve to keep meditating on the question till I should find a purely arithmetic and perfectly rigorous foundation for the principles of infinitesimal analysis.”
p, 125
Stetigkeit und irrationale Zahlen (1872)
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Richard Dedekind 13
German mathematician 1831–1916Related quotes

The Differential and Integral Calculus (1836)

Source: Examples of the processes of the differential and integral calculus, (1841), p. 237; Lead paragraph of Ch. XV, On General Theorems in the Differential Calculus,; Cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52
Source: 1960s, The meaning of the twentieth century: the great transition, 1964, p. 126

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IIII.37, The Arrow. p. 54
1921 - 1930, Pedagogical Sketch Book, (1925)

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The Differential and Integral Calculus (1836)

Footnote: The apparent advantage of the generality of this definition of number disappears as soon as we consider complex numbers. According to my view, on the other hand, the notion of the ratio between two numbers of the same kind can be clearly developed only after the introduction of irrational numbers.
Stetigkeit und irrationale Zahlen (1872)
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 427

Tobin, James. " Estimation of relationships for limited dependent variables http://cowles.econ.yale.edu/P/cp/p01a/p0117.pdf." Econometrica: journal of the Econometric Society (1958): 24-36.
1950s-60s