What is "Mathematics"?

To answer a question Bill Kerr asked on his blog:
http://billkerr2.blogspot.com/2008/02/what-is-maths.html

A recent, personal, epiphany came when I realized that the mathematics which I experience is the selective ignoring of detailed qualitative information so that one can concentrate on the quantitative properties of a problem one wishes to solve, or find an answer to a proposed question. I'm constraining my answer to the applying of mathematics as the purpose for teaching math, not just as teaching "thinking". Studying rhetoric and philosophy also teaches "thinking".

We measure a coast line for reasons of property ownership or weather effects or such not, regardless that the physical length of where the water meets the land changes numerous times every fraction of a second in numerous places. We compare apples to apples vs. apples to oranges even though no two apples are precisely the same.

To address the physical exercise analogy, our muscles are designed to remember what they need to remember as they have for thousands of years as used every day. Often what we learn in school is used once and infrequently after that. Perhaps if students in school were required to "start, and maintain for a long period, a profitable business" they might be compelled to practice what they've learned more frequently.

The interest in developing skills in mathematics might arrive more through the nature and personal relevance of the questions asked rather than the question of the relevance of learning how to solve them. Maybe we should start with probability theory and statistics rather than geometry so that the population can better understand when someone asserts something "is" a fact that it really "is" a fact (even better if drawn from current events). At least, fewer would lose their quantitative money at casinos. ;-)

Geometry was great when the industrial age needed engineers to change our physical world.

Probability is greater in a world where everyone has a global microphone, where everyone competes for global resources, where everyone can make micro level changes in their lives which have an accumulated global impact (in many domains) so that "facts" can quickly dissolve unnoticed into shades of gray in our only, shared, moment-by-moment ever changing world.

Even if you "don't do math", you can be sure that global markets, multinational corporations, national governments, insurance companies, university survey researchers, and marketing firms are "probability" and "mathematically" measuring you every moment of every day ... and even using those nasty "quadratic equations" to do so. :-)