A Quote by David Hilbert

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.

David Hilbert

Quote Topics

Arithmetic Axioms Development Fundamental Fundamental Principles Geometry Like Logical Number Only Principles Requires Simple Small

Quote Author

David Hilbert
German - Mathematician
January 23, 1862 - February 14, 1943

In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.

Jean-Victor Poncelet

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.

Eric Temple Bell

Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!

Jean Dieudonne

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

Carl Friedrich Gauss

America is conservative in fundamental principles... but the principles conserved are liberal and some, indeed, are radical.

Gunnar Myrdal

The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.

Hans Reichenbach

The circle is the fundamental geometry of open human communication.

Harrison Owen

Masonry, according to the general acceptation of the term, is an art founded on the principles of geometry, and devoted to the service and convenience of mankind. But Freemasonry, embracing a wider range and having a nobler object in view, namely, the cultivation and improvement of the human mind, may with more propriety be called a science, inasmuch as, availing itself of the terms of the former, it inculcates the principles of the purest morality, though its lessons are for the most part veiled in allegory and illustrated by symbols.

William Howard Taft

The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?

Rene Thom

Everything in life is built on principles - plants, seas, birds, all of the natural elements of nature, they all follow and obey certain basic fundamental principles.

Myles Munroe

The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.

Isaac Newton

Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.

Arthur Cayley

Principles don't die. They aren't here one day and gone the next. They can't be destroyed by fire, earthquake or theft. Principles are deep, fundamental truths, classic truths.

Stephen Covey

What makes it [economics] most fascinating is that its fundamental principles are so simple that they can be written on one page, that anyone can understand them, and yet very few do.