A Quote by Hans Reichenbach

We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.

Hans Reichenbach

Quote Topics

Aspects Axioms Exists Having Mathematics No Problem Only Problem Satisfied Shall Shown Special Treat Truth Visualization

Quote Author

Hans Reichenbach
Philosopher
September 26, 1891 - April 9, 1953

Pure geometrical regularity gives a certain pleasure to men troubled by the obscurity of outside appearance. The geometrical line is something absolutely distinct from the messiness, the confusion, and the accidental details of existing things.

T. E. Hulme

With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.

Niels Henrik Abel

...to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.

Carl Gustav Hempel

The laws of Nature are written in the language of mathematics...the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.

Galileo Galilei

A few rules include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the art of persuading.

Blaise Pascal

This simple idea served to provide information on the geometrical shape of reacting molecules, and I was able to make the role of the frontier orbitals in chemical reactions more distinct through visualization, by drawing their diagrams.

Kenichi Fukui

Next comes the realist phase ("After all, from a purely geometrical point of view a cat is only a tube with a door at the top.")

Terry Pratchett

All conceptions in the game of chess have a geometrical basis.

Eugene Znosko-Borovsky

Population, when unchecked, increases in a geometrical ratio.

Thomas Malthus

We cannot ... prove geometrical truths by arithmetic.

Aristotle

Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.

Ivars Peterson

No Roman ever died in contemplation over a geometrical diagram.

Alfred North Whitehead

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.