Magic in Mathematics I

"Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skillful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures."(Johann F Herbart, 1890)

"The mystery that clings to numbers, the magic of numbers, may spring from this very fact, that the intellect, in the form of the number series, creates an infinite manifold of well distinguishable individuals. Even we enlightened scientists can still feel it e.g. in the impenetrable law of the distribution of prime numbers." (Hermann Weyl, "Philosophy of Mathematics and Natural Science", 1927)

"Mathematics is not a compendium or memorizable formula and magically manipulated figures." (Scott Buchanan, "Poetry and Mathematics", 1929)

"There seems to be striking similarities between the role of economic statistics in our society and some of the functions which magic and divination play in primitive society." (Ely Devons, "Essays in Economics", 1929)

"[…] the social scientist who lacks a mathematical mind and regards a mathematical formula as a magic recipe, rather than as the formulation of a supposition, does not hold forth much promise. A mathematical formula is never more than a precise statement. It must not be made into a Procrustean bed - and that is what one is driven to by the desire to quantify at any cost. It is utterly implausible that a mathematical formula should make the future known to us, and those who think it can, would once have believed in witchcraft. The chief merit of mathematicization is that it compels us to become conscious of what we are assuming." (Bertrand de Jouvenel, "The Art of Conjecture", 1967)

"Symbols, formulae and proofs have another hypnotic effect. Because they are not immediately understood, they, like certain jokes, are suspected of holding in some sort of magic embrace the secret of the universe, or at least some of its more hidden parts." (Scott Buchanan, "Poetry and Mathematics", 1975)

"Mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. Mathematics is one of the eternal truths and, as such, raises the spirit to the same level on which we feel the presence of God." (Malba Tahan & Patricia R Baquero, "The Man Who Counted", 1993)

"Number theory [...] is a field of almost pristine irrelevance to everything except the wondrous demonstration that pure numbers, no more substantial than Plato's shadows, conceal magical laws and orders that the human mind can discover after all." (Sharon Begley, "New Answer for an Old Question", Newsweek, 1993)

"In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us?" (Ian Stewart, "The Magical Maze: Seeing the World Through Mathematical Eyes", 1997)