If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

— John Von Neumann

## Off-limits Mathematics And Science quotations

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.

Young man, in mathematics you don't understand things. You just get used to them.

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

### Where there is matter, there is geometry.

What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.

To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

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

Science and art sometimes can touch one another, like two pieces of the jigsaw puzzle which is our human life, and that contact may be made across the boderline between the two respective domains.

In order to solve this differential equation you look at it until a solution occurs to you.

The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.

### The mathematical sciences particularly exhibit order symmetry and limitations;

and these are the greatest forms of the beautiful.

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.

When you can measure what you are speaking about, and express it in numbers, you know something about it.

Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.

If your experiment needs statistics, you ought to have done a better experiment.

Creativity is essential to particle physics, cosmology, and to mathematics, and to other fields of science, just as it is to its more widely acknowledged beneficiaries - the arts and humanities.

### I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians.

The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers.

If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.

### Mathematics is not something that you find lying around in your back yard.

It's produced by the human mind. Yet if we ask where mathematics works best, it is in areas like particle physics and astrophysics, areas of fundamental science that are very, very far removed from everyday affairs.

[Kepler] preferred the hard truth to his dearest illusions, and that is the heart of science.

I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.

The general mental qualification necessary for scientific advancement is that which is usually denominated "common sense," though added to this, imagination, induction, and trained logic, either of common language or of mathematics, are important adjuncts.

### The purpose of computing is insight, not numbers.

The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization.

All the mathematical sciences are founded on relations between physical laws and laws of numbers.

The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generations adds a new story to the old structure.

One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.

But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius.

Mathematical Knowledge adds a manly Vigour to the Mind, frees it from Prejudice, Credulity, and Superstition.

All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.

### Obvious is the most dangerous word in mathematics.

The essential fact is that all the pictures which science now draws of nature, and which alone seem capable of according with observational facts, are mathematical pictures.