Algebra/What is math, exactly?

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Of all the subjects taught in schools throughout the world, Mathematics is possibly the one which has collected the image of being most feared and disliked.

So what is math? What makes it so different from other areas of study? And more importantly, why on earth do you need to know about it?

[edit] Definition

Math

The science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.

This definition, from Merriam-Webster's dictionary, is quite complete. But to simplify, it might be easier to think of math as using numbers and symbols to solve various quantifiable problems. That word quantifiable just means countable; 95% of the math most people will ever use is really just re-arranging numbers to tell them something useful. 30 miles at 55 miles per hour, how long will it take? 6 square meters of fabric, how many 10 centimeter squares? Math in some sense probably began in some vague prehistory with scratch marks in dirt or piles of stones. But now, some many thousands of years later, math is secretly at the core of modern human life. Were it not for the advances of a great many mathematicians (beginning with those dirt-scratchers) through history, we would not have the means to construct lasting buildings, roads or bridges, mechanized transportation, or digital entertainment such as the computer from which you are likely accessing this document. So even though you don't see numbers and calculations printed on everything that used them, the existence of an enormous part of our lives depends on this re-arrangement of numbers and symbols.

more later