Study actively. Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
Paul R. Halmos
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
G.H.Hardy
Mathematics is the art of giving the same name to different things.
Henri Poincaré
The essence of mathematics is its freedom.
Georg Cantor
And I'll go even further and say that mathematics, this art of abstract patternmaking — even more than storytelling, painting, or music  is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical patternrecognition machines and mathematics is nothing less than the distilled essence of who we are.
Paul Lockhart

Yearling
× 5Dec 22

CriticJan 6, 2021

SupporterNov 6, 2016

AutobiographerApr 26, 2016
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