What is Math?    

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

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

 Mathematics is a language.

Gibbs, Josiah Willard. 1839-1903.
American mathematician and physicist.

 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

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

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

More quotes on the nature of  Mathematics  http://math.furman.edu/cgi-bin/randquote.pl  

What is mathematics?   Most people would say it has something to do with numbers, but numbers are just one type of mathematical structure.   Saying "math is the study of numbers" (or something similar) is like saying that "zoology is the study of giraffes".  Math may be better thought of as the study of patterns, but this too falls short...

The more I study math, the more I wonder about what exactly math is.  Actually nobody knows.   It seems to be a product or our minds, and yet reflects the external universe with uncanny accuracy.   A mathematician develops a mathematical theory for its aesthetic unworldly beauty and it's compelling evolution, with no thought of how it might be applied to the world.    A century later a physicist finds this theory to be perfect to use as a framework to express his physics (this sort of thing happens frequently).   Pretty weird how intimately connected our innermost "mind" and the outermost "universe" really are.   This is a profound mystery!

Bruce Bennett, my advisor in grad school, defines mathematics as "unified consciousness theory".   As you come to master a branch of mathematics, it's as though you've grown a new abstract organ of perception through which you may then view the world.  You've grown a new "mind's eye" that can perceive realities literally inconceivable without this new organ of perception.

Rafael Espericueta
Professor of Mathematics
Bakersfield College


Mathematics as Art