Paul Dirac Quotes

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

Modern mathematics, that most astounding of intellectual creations, has projected the mind's eye through infinite time and the mind's hand into boundless space.

That sometimes clear ... and sometimes vague stuff ... which is ... mathematics.

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.

But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.

Mathematics is concerned only with the enumeration and comparison of relations.

The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.

But think of Adam and Eve like an imaginary number, like the square root of minus one: you can never see any concrete proof that it exists, but if you include it in your equations, you can calculate all manner of things that couldn't be imagined without it.

Still more astonishing is that world of rigorous fantasy which we call mathematics.

Yet what are all such gaieties to me whose thoughts are full of indices and surds?

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

Only Numbers. Pure math. You have to accustom yourself to thinking that way.

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

Mathematics is the abstract key which turns the lock of the physical universe.

The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilised of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.

Nonmathematical people sometimes ask me, “You know math, huh? Tell me something I’ve always wondered, What is infinity divided by infinity?” I can only reply, “The words you just uttered do not make sense. That was not a mathematical sentence. You spoke of ‘infinity’ as if it were a number. It’s not. You may as well ask, 'What is truth divided by beauty?’ I have no clue. I only know how to divide numbers. ‘Infinity,’ ‘truth,’ ‘beauty’—those are not numbers.

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular 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.

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

If equations are trains threading the landscape of numbers, then no train stops at pi.

Mathematics deals exclusively with the relations of concepts to each other without consideration of their relation to experience.

The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes a song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures.

In philosophy, the principles are more interesting than the examples. In literature, the examples are more interesting than the principles.

The Good Lord made all the integers; the rest is man's doing.