Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. An abstract representational system used in the study of numbers, shapes, structure and change and the relationships between these concepts.
 n. A person's ability to count, calculate, and use different systems of mathematics at differing levels.
from the GNU version of the Collaborative International Dictionary of English
 n. That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations.
from The Century Dictionary and Cyclopedia
 n. The science of quantity; the study of ideal constructions (often applicable to real problems), and the discovery thereby of relations between the parts of these constructions, before unknown.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
Etymologies
Examples

A reflection of their fundamental philosophy, the Pythagoreans invented the term mathematics, from the Greek word mathema, which meant “science.”

Considered a child prodigy, he went to Harvard and graduated, then he got his PhD in mathematics from the University of Michigan.

Education: Bachelor's degree in mathematics from the University of Delhi and an MBA in marketing and finance from the Indian Institute of ManagementAhmedabad.

Regarding an underlying mathematical edifice, a possible analogy in mathematics is the existence of noncomputable numbers, these numbers have no deterministic, no algorithmic description, yet they exist.

Only a philosophical topology, analogous to what in mathematics is defined as analysis situ (analysis of site), in opposition to analysis magnitudinis

The question asked which branch of mathematics comes from the Greek word for reunite.

We compose our systems of music, which we call mathematics, that are model systems of internal consistency.

Society, who, accepting Bacon's demand for certainty and not finding it in the hypothetical physics, empha  sized the necessity for a more Archimedean approach: what they called mathematics and what today might be termed mathematical physics.

Things which may at first sight appear comparatively valueless in education  such as the study of the dead languages, and the relations of lines and surfaces which we call mathematics  are really of the greatest practical value, not so much because of the information which they yield, as because of the development which they compel.

I will now explain my meaning by literal examples, leaving aside all purely abstract reasoning, which I call the mathematics of thought.
Louises commented on the word mathematics
A person steps into the road, turns, sees a truck about to hit him, seems to freeze. The freezing is the amazingly quick brain making its honourable start on the avoidance mathematics, the geometry of getting out of the way. And even the amazingly quick brain is too slow. The first trajectory calculations are barely  BAM! Goodnight. From "The Last Werewolf" by Glen Duncan.
March 23, 2012
PossibleUnderscore commented on the word mathematics
"Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry."
Bertrand Russell
Yes. Yes indeed.
April 24, 2010
oroboros commented on the word mathematics
9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
9876 × 9 + 4 = 88888
98765 × 9 + 3 = 888888
987654 × 9 + 2 = 8888888
9876543 × 9 + 1 = 88888888
98765432 × 9 + 0 = 888888888
987654321 x 9  1 = 8888888888
From: Futility Closet
(BTW, 80/81 = .987654321 with rounding)
July 15, 2008