12 December 2021

On Numbers (1700-1799)

"To understand the theory of chance thoroughly, requires a great knowledge of numbers, and a pretty competent one of Algebra." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)

"Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being." (Gottfried Leibniz, 1702)

"The probability of an Event is greater, or less, according to the number of Chances by which it may Happen, compar’d with the number of all the Chances, by which it may either Happen or Fail. […] Therefore, if the Probability of Happening and Failing are added together, the Sum will always be equal to Unit." (Abraham De Moivre, "The Doctrine of Chances", 1718)

"From this it follows that the idea of positive or negative is added to those magnitudes which are contrary in some way. […] All contrariness or opposition suffices for the idea of positive or negative. […] Thus every positive or negative magnitude does not have just its numerical being, by which it is a certain number, a certain quantity, but has in addition its specific being, by which it is a certain Thing opposite to another. I say opposite to another, because it is only by this opposition that it attains a specific being (Bernard le Bouyer de Fontenelle, "Éléments de la géométrie de l'Infini", 1727)

"[…] the sciences that are expressed by numbers or by other small signs, are easily learned; and without doubt this facility rather than its demonstrability is what has made the fortune of algebra." (Julien Offray de La Mettrie, "Man a Machine", 1747)

"Round numbers are always false." (Samuel Johnson, [Letter to Thomas Boswell], 1778)

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