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 ...

 Consume Fragments of Truth

At the outset do not be worried about this big question—Truth. It is a very simple matter if each one of you starts with the desire to get as much as possible. No human being is constituted to know the truth, the whole truth, and nothing but the truth; and even the best of men must be content with fragments, with partial glimpses, never the full fruition. In this unsatisfied quest the attitude of mind, the desire, the thirst—a thirst that from the soul must arise!—the fervent longing, are the...

 Neoteny in Humans

...the concept of "neoteny"—the retention of juvenile features into adult life. It is a commonplace of human evolution that the transition from Australopithecus to Homo and from Homo habilis to Homo erectus and thence to Homo sapiens all involved prolonging and slowing the development of the body so that it still looked like a baby when it was already mature. The relatively large brain case and small jaw, the slender limbs, the hairless skin, the unrotated big toe, the thin bones, even the ex...