24 Quotes by Paul Lockhart

So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It’s not at all like science. There’s no experiment I can do ... The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.

... This is a major theme in mathematics: things are what you want them to be. You have endless choices; there is no reality to get in your way.On the other hand, once you have made your choices then your new creations do what they do, whether you like it or not. This is the amazing thing about making imaginary patterns: they talk back!

... That little narrative is an example of the mathematician’s art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it’s fascinating, it’s fun, and it’s free!

If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.

Mathematicians enjoy thinking about the simplest possible things, and the simplestpossible things are imaginary.

Simplicio: Are you really trying to claim that mathematics offers no useful or practical applications to society? Salviati: Of course not. I'm merely suggesting that just because something happens to have practical consequences, doesn't mean that's what it is about. Music can lead armies into battle, but that's not why people write symphonies. Michelangelo decorated a ceiling, but I'm sure he had loftier things on his mind.

I don't see how it's doing society any good to have it's members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.

If teaching is reduced to mere data transmission, if there is no sharing or excitement and wonder, if teachers themselves are passive recipients of information and not creators of new ideas, what hope is there for their students?

SIMPLICIO: ... You have to [learn to] walk before you can run.SALVIATI: No, you have to have something you want to run toward.