If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it, what does the formula teach me?

If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it, what does the formula teach me?

De Magistro X, 23.

The good Christian should beware of mathematicians, and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

De Genesi ad
Litteram, Book II,
xviii, 37 [Note:
mathematician =
astrologer]

Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true. God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exist.

The City of God.

The modern, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers not because it is abstract, but because it is a representation of actual things.

In N. Rose,
Mathematical Maxims
and Minims, Raleigh
NC: Rome Press Inc.,
1988.

It is a pleasant surprise to him (the pure mathematician) and an added problem if he finds that the arts can use his calculations, or that the senses can verify them, much as if a composer found that sailors could heave better when singing his songs.

In J. R. Newman
(ed.), The World of
Mathematics, New
York: Simon and
Schuster, 1956.

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.

The biologist can push it back to the original protist, and the chemist can push it back to the crystal, but none of them touch the real question of why or how the thing began at all. The astronomer goes back untold millions of years and ends in gas and emptiness, and then the mathematician sweeps the whole cosmos into unreality and leaves one with mind as the only thing of which we have any immediate apprehension. Cogito ergo sum, ergo omnia esse videntur. All this bother, and we are no further than Descartes. Have you noticed that the astronomers and mathematicians are much the most cheerful people of the lot? I suppose that perpetually contemplating things on so vast a scale makes them feel either that it doesn't matter a hoot anyway, or that anything so large and elaborate must have some sense in it somewhere.

With R. Eustace, The
Documents in the
Case, New York:
Harper and Row,
1930, p. 54.

Of all the intellectual faculties, judgment is the last to mature. A child under the age of fifteen should confine its attention either to subjects like mathematics, in which errors of judgment are impossible, or to subjects in which they are not very dangerous, like languages, natural science, history, etc.

If you would make a man happy, do not add to his possessions but subtract from the sum of his desires.

In H. Eves, Return
to Mathematical
Circles, Boston:
Prindle, Weber and
Schmidt, 1988.

I cannot do it without comp[u]ters.

The Winter's Tale.