Before he retired, my dad was a physicist. When as a teenager I approached him with questions about my algebra homework, I got more than I bargained for. I remember him casting an appraising eye on my textbook, the better I assumed to address my questions in an appropriate fashion, before remarking, "It is obvious that the author of this textbook knows nothing of mathematics. I really must speak with your teacher."

Not what I had in mind.

His subsequent interest in my mathematical education was the source of some tense moments. He cared more for math than for my self esteem and sometimes had a hard time understanding how I could not understand. His first language is Norwegian, and he worked hard to eliminate the inflections of that language from his spoken English, but when agitated, as he was by my trouble simplifying algebraic expressions by factoring, his voice would rise, and he would suddenly sound scary and foreign. The sounds of our algebra sessions carried to other parts of the house and I remember my mom peering into the room we were working in while nervously drying her hands on a dish towell. I wished she would interrupt but she didn't. How could I concentrate with her just standing there and him talking loud at me, his voice rising sharply in that weird Norwegian way at the end of his emphatic speech acts?

But I received a grounding in algebra. It's its own reward, I think, but once in awhile you get to amaze the uninitiated with your mystical powers. Today, in a meeting, someone wanted to know the product of 54 and 46. While someone else began reaching for a calculator, I announced, "Two thousand four hundred and eighty four." When a few seconds later the guy with the calculator verified my answer, jaws sagged, and I think my colleagues now regard me as a genius, or possibly as an "idiot savant" along the line of the Dustin Hoffman character in *Rain Man*. But it is really just the simplest algebra. It just happens that 54 is four more, and 46 four less, than fifty. So you have an instance of (a + b)(a - b) where a = 50 and b = 4. Since (a + b)(a - b) = a^{2} - b^{2}, it follows that 54 x 46 = 50^{2} - 4^{2}, which is not too hard to do in your head. If the problem had been the product of 54 and 44, the fellow with the calculator would have gotten there first.

Well, maybe not: 54 x 44 = (44 x 50) + (44 x 4) = 1/2 (4400) + 176 = 2376. It was from my dad's way of teaching algebra that I learned to think like this. Before, algebra had been to me a kind of incomprehensible code, the whole object of which was to memorize certain abstruse manipulations that allowed you to "solve" meaningless "problems." The realization that it is arithmetic generalized--*that* made all the difference.

## Comments