Arthur Cayley Quotes

Arithmetic! Algebra! Geometry! Grandiose trinity! Luminous triangle! Whoever has not known you is without sense!

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry.

Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

... preliminary accounting, banking and surveying (known as arithmetic, algebra and geometry).

The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes.

I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry.

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.

The only royal road to elementary geometry is ingenuity.

There are no sects in geometry.

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

The ludicrous state of solid geometry made me pass over this branch.

The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system.

The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.

Mathematics commands all my respect, but I have no use for engines.

Geometry draws the soul towards truth.

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.

Geometry is knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them.

Galois read the geometry from cover to cover as easily as other boys read a pirate yarn.

Symmetrical equations are good in their place, but ' vector ' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.

Where there is matter, there is geometry.

Geometry is the foundation of all painting.

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.

My basic mathematics is rather weak, so when some of the theories are broken into equations, I get rather lost.