My family and I were recently discussing what makes people good at math. My son Nathaniel, who’s in his early thirties, brought up something he read in Malcolm Gladwell’s book Outliers. Gladwell talks about a woman in her mid twenties named Renee who’s trying to solve a math problem as part of a research project. Renee is sitting at a computer that allows you to type in x and y axis values to produce a curve. It’s basic rise over run math stuff that we all learned in junior high school or high school (but nearly all of us have since forgotten).
If you’re like me and you’ve forgotten, Gladwell provides a brief example. If the value of the rise on the y axis = 5, and the value of the run on the x axis = 5, then the slope = 1. Because the rise over run is 5 over 5, and 5/5 = 1.
So this woman Renee is sitting at the computer trying to solve a problem. And while she’s doing this, a Cal Berkeley professor and researcher named Alan Schoenfeld is sitting next to her. Schoenfeld knows the problem Renee is trying to solve is impossible. But she wasn’t told that it’s impossible. What she was told, was to enter values that will create a line that is perfectly vertical. But the problem is impossible because a vertical line requires a rise value of infinity and a run value of 0. And infinity divided by 0 doesn’t produce a number.
So she’s sitting there at this computer. And she starts entering in values. And she fiddles around. And she enters some more values. And then she fiddles some more. The whole while she’s talking to herself. And as she fiddles and experiments, her values for y get larger and larger. And the larger they get, the closer the line gets to the y axis. But no matter how large a value she assigns to y it never gets there.
Finally, after twenty-two minutes of trial and error, Renee experiences a eureka moment and she says, Continue reading