Quotations collected below all reflect on perception of Mathematics by various people over a few hundred years history. (My own thoughts could be found in my Manifesto and the What is What? section of the site.)

Proclus (412-485) had this to say:

The Pythagoreans considered all mathematical sciences to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics (astronomy, A.B.) magnitude inherently moving.

Obviously, in the 2500 years since Pythagoras when music was still considered a mathematical science, both human perception of and our attitude towards, mathematics underwent a tremendous metamorphosis. Below I list several quotations - definitions of mathematics - but this is not a quotation page per se. Presenting different views with quotations appears to me less personal and more authoritative. Could you please check the boxes against those quotations you approve of and then press the Submit button at the bottom of the page.

math-e-mat-ics n. (used with a sing. verb). The study of the measurement, properties, and relationships of quantities, using numbers and symbols. [From Middle English mathematik, from Old French mathematique, from Latin mathematica, from Greek mathematike (tekhne)]

The American Heritage Dictionary
Relevant quotations

math-e-mat-ics n. ... the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.

Webster's New Collegiate Dictionary
Relevant quotations

Mathematics is a language.

Gibbs, Josiah Willard. 1839-1903.
American mathematician and physicist.
A story I heard.

To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

Richard Feynman. 1918-1988.
American physicist.
The Character of Physical Law
Relevant quotations

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Bertrand Russell. 1872-1970
British philosopher, mathematician.
Mysticism and Logic
Relevant quotations

All science requires Mathematics. The knowledge of mathematical things is almost innate in us... This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

Roger Bacon. 1214-1294
English philosopher, scientist.
Opus Maius

We do not teach arithmetic in Kindergarten. A knowledge of mathematics is not necessary to a four year old. Any premature instruction arrests development.

Philosophy of Froebel Kindergarten.
Pictured Knowledge, p899, several editions 1916-1927
Marshall Hughes Co.

AHD Webster Gibbs Feynman Russell Bacon Froebel

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