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“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”
― A Mathematician's Apology
― A Mathematician's Apology
“The philosopher treats a question; like an illness.”
― Philosophical Investigations
― Philosophical Investigations
“No one can build you the bridge on which you, and only you, must cross the river of life. There may be countless trails and bridges and demigods who would gladly carry you across; but only at the price of pawning and forgoing yourself. There is one path in the world that none can walk but you. Where does it lead? Don’t ask, walk!”
― Schopenhauer as Educator
― Schopenhauer as Educator
“I leave Sisyphus at the foot of the mountain. One always finds one's burden again. But Sisyphus teaches the higher fidelity that negates the gods and raises rocks. He too concludes that all is well. This universe henceforth without a master seems to him neither sterile nor futile. Each atom of that stone, each mineral flake of that night-filled mountain, in itself, forms a world. The struggle itself toward the heights is enough to fill a man's heart. One must imagine Sisyphus happy.”
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“Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”
― A Mathematician's Apology
― A Mathematician's Apology
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