All the Ways of Intuiting 1729

Stanislas Dehaene brings up the Ramanujan-G.H.Hardy anecdote concerning the number 1729. The idea of running through the cubes of all integers from 1 to 12 in order to arrive at Ramanujan's spontaneous recognition of 1729 as the smallest positive integer that can be written in two distinct ways as the sum of two integral cubes is inappropriate and obscures the workings of the naive mathematical mind. To be sure, a computer-mind could come up with that list at a wink. But what would induce it ...

 A Novel Way to Teach the Constitution

Daniel Kunitz is a friend of mine from college. He's spent his life as an innovative junior and senior high school social sciences teacher. Want the students to understand the Constitution of the United States? You could have them read it, Article by Article, and then discuss it in class but, sadly, this will put most of them to sleep. Or you could try the Kunitz method: you forbid the students to read the Constitution. Instead, you assign them, two for each state, to attend a Constitutional ...