Quotes About Mathematics

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

The primary concern of mathematics is number, and this means the positive integers…. Mathematics belongs to man, not God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer exists, he should show how to find it. If God has mathematics of his own that needs to be done, let him do it himself.

Brouwer's criticisms of classical mathematics were concerned with what I shall refer to as "the debasement of meaning".

More important than being able to do mathematics is to be sure the applications are meaningful.

The reason for this was not that the subject was simple enough to be explained without mathematics, but rather that it was much too involved to be fully accessible to mathematics.

A mathematical truth is timeless, it does not come into being when we discover it.

Uma verdade matemática é intemporal, não ganha existência quando a descobrimos. Contudo, sua descoberta é um evento bem real, pode ser uma emoção, como um grande presente de uma fada.

Q.E.D. [Quod erat demonstrandum: Which was to be proved.]

The laws of nature are but the mathematical thoughts of God.

There is no Royal Road to Geometry.

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

Let me end on a more cheerful note. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

We cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors.

Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius.

The mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.

Naturally, we do use mathematics in everyday physics to evaluate the results of the laws of nature, to apply the conditional statements to the particular conditions which happen to prevail or happen to interest us. In order that this be possible, the laws of nature must already be formulated in mathematical language.

It is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.

Definition of a Statistician: A man who believes figures don't lie, but admits than under analysis some of them won't stand up either.

Definition of Statistics: The science of producing unreliable facts from reliable figures.

[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.

Math education has changed over the years. In the 19th century, they taught spherical trigonometry because one of the biggest applications of mathematics was navigating the ocean. This is no longer so relevant.

I'd rather have a pencil and paper and do all my own calculations rather than rely on a machine. And I'll do most calculations in double digit multiples as quick as the machine.

Acting is mathematics for me. I do very little homework and rather rely on my imagination for playing a role.