On Numbers: Defining Numbers

“Number is the bond of the eternal continuance of things.” (Plato)

“Measure, time and number are nothing but modes of thought or rather of imagination.” (Baruch Spinoza, [Letter to Ludvicus Meyer] 1663)

"[…] if number is merely the product of our mind, space has a reality outside our mind whose laws we cannot a priori completely prescribe" (Carl F Gauss, 1830)

"Numbers are intellectual witnesses that belong only to mankind, and by whose means we can achieve an understanding of words." (Honore de Balzac)

"Numbers constitute the only universal language." (Nathanael West, “Miss Lonelyhearts”, 1933)

“[…] there are terms which cannot be defined, such as number and quantity. Any attempt at a definition would only throw difficulty in the student’s way, which is already done in geometry by the attempts at an explanation of the terms point, straight line, and others, which are to be found in treatise on that subject.” (Augustus de Morgan, “On the Study and Difficulties of Mathematics”, 1943)

“Numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.” (Hermann Weyl, “Mathematics and the Laws of Nature”, 1959)

“[…] numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things.” (Richard Dedekind, “Essays on the Theory of Numbers”, 1963)

“Numbers are not just counters; they are elements in a system.” (Scott Buchanan, “Poetry and Mathematics”, 1975)

“Number is therefore the most primitive instrument of bringing an unconscious awareness of order into consciousness.” (Marie-Louise von Frany, “Creation Myths”, 1995)