The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

Metaphysica 1-5

The whole is more than the sum of its parts.

Metaphysica 10f-1045a

Now that practical skills have developed enough to provide adequately for material needs, one of these sciences which are not devoted to utilitarian ends [mathematics] has been able to arise in Egypt, the priestly caste there having the leisure necessary for disinterested research.

Metaphysica, 1-981b

Meton: With the straight ruler I set to work

To make the circle four-cornered.

[Perhaps the first
allusion to the
problem of squaring
the circle]

The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning; and when they cannot it's a sign our knowledge of them is very small and confus'd; and when a Mathematical Reasoning can be had it's as great a folly to make use of any other, as to grope for a thing in the dark, when you have a Candle standing by you.

Of the Laws of
Chance (1692)

Referee's report: This paper contains much that is new and much that is true. Unfortunately, that which is true is not new and that which is new is not true.

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

Defendit numerus:There is safety in numbers.

In J. R. Newman
(ed.), *The World
of Mathematics,*
New York: Simon and
Schuster, 1956, p.
1452.

Like the crest of a peacock, like the gem on the head of a snake, so is mathematics at the head of all knowledge.

If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.

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

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

"Mathematics and History", Mathematical Intelligencer, v. 4, no. 4.