705 Quotes About Mathematics

For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.

The theory of permutations, like everything else, is best understood by staring hard at some non-trivial examples.

If you want to know the secrets of existence, do the math. There is no other way. There is only one truth, the truth of mathematics. It is the infallible, absolute truth. All truth-seekers come in the end to mathematics. Pythagoras got there first. It’s time for everyone else to join him and hear the Music of the Spheres. Are your ears attuned to the perfect notes of the universe? Only the gods can hear the divine music. Are you one of them?

We are not told, or not told early enough so that it sinks in, that mathematics is a language, and that we can learn it like any other, including our own. We have to learn our own language twice, first when we learn to speak it, second when we learn to read it. Fortunately, mathematics has to be learned only once, since it is almost wholly a written language.

Mathematics: The language of the mathematicians, by the mathematicians, for the mathematicians.

A successfully chosen name is a bridge between scientific knowledge and common sense, between new experience and old habits. The conceptual foundation of any science consists of a complicated network of names of things, names of ideas, and names of names. It evolves itself, and its projection on reality changes.

As long as I could connect every new thing I learned to this universe, I had an easy time with math.And I noticed that classmates who had problems with math weren’t struggling with math; they werestruggling with connections. They were trying to memorize equations, but no one had successfullyshown them how those equations connect with everything they had already learned. They weredoomed

Jack had wondered how geometers could be so inventive as to produce so many types and families of curves. Later he had come to perceive that of curves there was no end, and the true miracle was that poets, or writers, or whoever it was that was in charge of devising new words, could keep pace with those hectic geometers, and slap names on all the whorls and snarls in the pages of the Doctor's geometry-books.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.