Shape
Jordan Ellenberg
Introduction

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 middleaged Wordsworth! Or to let the poet speak: Mighty is the charm of those abstractions to a mind beset With images, and haunted by itself.
Foreword

Dante namechecks 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."

Ben BlumSmith describes the problem: for students to really feel the fire of math, they have to experience the gradient of confidenceâ€”the feeling of moving from something obvious to something notobvious, 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.