> I have never been asked to do anything this in a math class. This is a tragic comment. It is also true. American children waste their time and their brains i

> I have never been asked to do anything this in a math class. This is a tragic comment. It is also true. American children waste their time and their brains in American math classes for about 8 years each. They learn to multiply and maybe solve a quadratic equation. "Equations are sometimes called theorems," and that's it. And it's not getting better; as a culture, we don't understand or respect math so we don't support it. Modern mathematicians don't memorize or drill steps. We don't just find a bigger number each day by adding one. We hold our problems, trace them, ask ourselves how the proof should be designed and figure out where the problems in the logic are. If you've got 2n points in a line, how many ways can you draw a curve from one point to another such that you match them all up and none of the curve intersect? What about if they're in a circle -- is the answer different? How do you characterize a straight line if you're in a non-Euclidean surface? What's the right definition of straight -- should straight mean "direction of derivative is in direction of line" or "shortest distance" or what? And if we're talking about points on a grid, how should distance be measured anyway? Do we have the right definitions to solve our problem? Distance from streetcorner to streetcorner by cab in Manhattan is different than distance as the crow flies is different than "distance" through time and space; how are the concepts consistent, then? Formulas are just shorthand for relationships. We don't teach students the relationships or the thinking in the US. That's why my Romanian advisor would ask our graduate algebra class, "You should have learned this in high school, no? No... Hmph." American school math is like prison, a holding cell until release that merely increases the likelihood you'll do poorly in the future.