The Rate of Change of a Rate of Change

In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the word 'simplest'. It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = K(d^2x/dy^2) much less simple than 'it oozes', of which it is the mathematical statement. The physicist reverses this judgment, and his statement ...

 Mathematics Should be Taught Like Art

Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren't even told that such paintings existed. Pretty soon you'd be asking, why study art? That's absurd, of course, but it's surprisingly close to the way we teach children mathematics. In elementary and middle school and even into high school, we hide math's great masterpieces from students' view. The arithmetic, algebraic equati...