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“ Math is the painting you can climb into, the song whose notes you can lean on. It is the creation of the searching, unsatisfied mind that, discouraged by the physical world, creates another. This new world is perfect and can be explained elegantly. There are no wars, only equality signs. If a number gets too complicated, we give it a letter (pi, e, phi). If we don’t know the number, we give it a variable (x). If the number doesn’t exist, we pretend it does (i). We make things up so we can conquer them simply and elegantly after a journey — playful or strenuous. In a way, mathematicians are not only idealists, but escapists. Unlike other artists who create things to respond to life — Picasso’s “Guernica”, Dvorak’s “New World” — math creates its own world wanting to abandon this one. But whether math is created to show the world how perfect life can be or to pretend this one doesn’t exist, math is surely an art, and not something that can be confined to the green and black of my calculator screen. ”

“ To some students, getting cues from the teacher rather than thinking about the math has become such an ingrained habit that it is their entire modus operandi when doing math with an expert around (teacher, tutor, parent, peer, etc.). They usually have lost faith in their ability to have math actually make sense to them, and this cueing has become their sole survival strategy. They regularly fail tests and have come to accept this, but they would rather fake you out than admit ignorance – understandable, since they often carry a feeling of stupidity arising from their lost faith, and admitting ignorance would mean exposing this supposed stupidity. So they watch you and produce the right answers more often than not. Not with any sense of trickery or getting over on anyone – often, they’re barely conscious of the game. But it’s how they survive. ”