ABSTRACT
Simple facts of arithmetic or geometry are often tested by common experience. If you throw six nuts into a basket, and then add ten more, you get the same total as if ten went in first, followed by six. The commutativity of addition is thus testable in a meaningful way. The same cannot be said for many of the results of mathematics.
What direct experience suggests that there are infinitely many prime numbers, or that the square root of two is not the quotient of two integers? Is the scarcity of solutions to the equation
