Definition:Mathematics

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An attempt at a definition

From Wikipedia:

Mathematics is the academic discipline, and its supporting body of knowledge, that involves the study of such concepts as quantity, structure, space and change. Other practitioners of mathematics maintain that mathematics is the science of pattern, and that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions. [1]


"Purity" from the webcomic XKCD


Contemporary Quip

Biologists think they're biochemists.
Biochemists think they're chemists.
Chemists think they're physicists.
Physicists think they're God.
God thinks he's a mathematician.


Notable Quotes

St. Augustine of Hippo

Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant.
- De Genesi ad Litteram (The Literal Interpretation of Genesis), 408 C.E. II, xvii, 37

The translation published in 1953: Morris Kline: Mathematics in Western Culture:

The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell.

A later and more currently accurate translation is given by J.H. Taylor in Ancient Christian Writers (1982):

Hence, a devout Christian must avoid astrologers and all impious soothsayers, especially when they tell the truth, for fear of leading his soul into error by consorting with demons and entangling himself with the bonds of such association.

The Latin word mathematici derives from the Greek meaning of "something learned" and referred mainly to astrologers. At the time, astrology was the main outlet for the talents of a mathematically-minded person, so the slur may have been more well-directed than a current interpretation may allow.

At least as recently as 1710, the word "mathematician" still meant "astrologer".


Galileo Galilei

Philosophy is written in that great book which ever lies before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language $\dots$ without which one wanders in vain through a dark labyrinth.


David Hilbert

One day, David Hilbert noticed that one of his students was no longer attending his lectures. He was told that the student had given up mathematics, and taken up poetry instead.

Hilbert replied:

"Good -- he did not have enough imagination to become a mathematician."


Albert Einstein

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.


Alfred Tarski

The view has become more and more common that the deductive method is the only essential feature by means of which the mathematical disciplines can be distinguished from all other sciences; not only is every mathematical discipline a deductive theory, but also, conversely, every deductive theory is a mathematical discipline $\dots$ We will not enter here into a discussion of the reasons in favor of this view, but merely remark that is is possible to put forward ponderable arguments in its support.
-- 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.): $\S 6.36$


Arthur Koestler

In the index to the six hundred odd pages of Arnold Toynbee's A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur $\dots$ yet their cosmic quest destroyed the mediaeval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.
-- Epigraph to Part $\text A$ of 1992: George F. Simmons: Calculus Gems


I see your "purity" and I raise you "circularity"