In a truly great ongoing column at The Opinionater, Steven Strogatz explains math, from the beginning….
At this stage in the series it’s time to shift gears, moving on from grade school arithmetic to high school math. Over the next few weeks we’ll be revisiting algebra, geometry and trig. Don’t worry if you’ve forgotten them all — there won’t be any tests this time around, so instead of worrying about details, we have the luxury of concentrating on the most beautiful, important and far-reaching ideas. Algebra, for example, may have once struck you as a dizzying mix of symbols, definitions and procedures, but in the end they all boil down to just two activities — solving for x and working with formulas. Solving for x is detective work. You’re searching for an unknown number, x. You’ve been handed a few clues about it, either in the form of an equation like 2x + 3 = 7, or, less conveniently, in a convoluted verbal description of it (as in those scary “word problems”). In either case, the goal is to identify x from the information given.