Quotes on Mathematics

A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?

The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.

Sometimes attaining the deepest familiarity with a question is our best substitute for actually having the answer.

Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.

In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.

Think! Think and wonder. Wonder and think. How much water can 55 elephants drink?

Mathematics is not only real, but it is the only reality.

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

My basic idea is that programming is the most powerful medium of developing the sophisticated and rigorous thinking needed for mathematics, for grammar, for physics, for statistics, for all the "hard" subjects.... In short, I believe more than ever that programming should be a key part of the intellectual development of people growing up.

It is more important that a proposition be interesting than that it be true. This statement is almost a tautology. For the energy of operation of a proposition in an occasion of experience is its interest and is its importance. But of course a true proposition is more apt to be interesting than a false one.

Mathematics is the key and door to the sciences.

I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.

Music is the pleasure the human mind experiences from counting without being aware that it is counting.

The method of "postulating" what we want has many advantages; they are the same as the advantages of theft over honest toil.

Zero is powerful because it is infinity’s twin. They are equal and opposite, yin and_x000D_ yang. They are equally paradoxical and troubling. The biggest questions in science_x000D_ and religion are about nothingness and eternity, the void and the infinite, zero and_x000D_ infinity. The clashes over zero were the battles that shook the foundations of philosophy,_x000D_ of science, of mathematics, and of religion. Underneath every revolution lay a_x000D_ zero – and an infinity.

To make a great dream come true, the first requirement is a great capacity to dream; the second is persistence.

... and it is probably that there is some secret here which remains to be discovered.

Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

Bridges would not be safer if only people who knew the proper definition of a real number were allowed to design them.

For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated unto use with sufficient dexterity, without the aid and intervening of the mathematics, of which sort are perspective, music, astronomy, cosmography, architecture, engineery, and divers others.

"It's very good jam," said the Queen. "Well, I don't want any to-day, at any rate." "You couldn't have it if you did want it," the Queen said. "The rule is jam tomorrow and jam yesterday but never jam to-day." "It must come sometimes to "jam to-day,""Alice objected. "No it can't," said the Queen. "It's jam every other day; to-day isn't any other day, you know." "I don't understand you," said Alice. "It's dreadfully confusing."