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 ...

 The Prefontal Cortex

Executive functions take place in the prefrontal cortex of the brain. I love the term that Stanislas Dehaene uses to describe this part of the brain—a global neuronal workspace. The prefrontal cortex is responsible for the ability to exchange information across the high-level areas of the brain, Dehaene says, so that our behavior can be guided by our accumulated knowledge. That’s the beauty and the purpose of executive functions: they enable us to control ourselves, to reflect deeply, and...