Good luck for shipwreck guy: depressed and hungry though he is, he consoles himself by working his way through Euclid's demonstrations one by one, tracing out the diagrams in the sand with a stick. That's just what it was like to be young, sensitive, poetic Wordsworth, writes middle-aged Wordsworth! Or to let the poet speak:
Mighty is the charm
of those abstractions to a mind beset
With images, and haunted by itself.#1076•
Foreword
Dante name-checks it in the Paradiso: "Like the geometer who gives his all trying to square the circle, and still can't find the idea he needs, that's how I was."#979•
Ben Blum-Smith describes the problem: for students to really feel the fire of math, they have to experience the gradient of confidence—the feeling of moving from something obvious to something not-obvious, pushed uphill by the motor of formal logic. Otherwise, we're saying, "Here is a list of axioms that seem pretty obviously correct; put these together until you have another statement that seems pretty obviously correct." It's like teaching somebody about Lego by showing them how you can make two little bricks into one big brick.
You can do that, and sometimes you need to, but it is definitely not the point of Lego.#997•