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“It is in this gesture of "going beyond," to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one-it is in this solitary act that one finds true creativity. All others things follow as a matter of course.”
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“Outsiders sometimes have an impression that mathematics consists of applying more and more powerful tools to dig deeper and deeper into the unknown, like tunnelers blasting through the rock with ever more powerful explosives. And that's one way to do it. But Grothendieck, who remade much of pure mathematics in his own image in the 1960's and 70's, had a different view: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration...the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it...yet it finally surrounds the resistant substance."
The unknown is a stone in the sea, which obstructs our progress. We can try to pack dynamite in the crevices of rock, detonate it, and repeat until the rock breaks apart, as Buffon did with his complicated computations in calculus. Or you can take a more contemplative approach, allowing your level of understanding gradually and gently to rise, until after a time what appeared as an obstacle is overtopped by the calm water, and is gone. Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.”
― How Not to Be Wrong: The Power of Mathematical Thinking
The unknown is a stone in the sea, which obstructs our progress. We can try to pack dynamite in the crevices of rock, detonate it, and repeat until the rock breaks apart, as Buffon did with his complicated computations in calculus. Or you can take a more contemplative approach, allowing your level of understanding gradually and gently to rise, until after a time what appeared as an obstacle is overtopped by the calm water, and is gone. Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.”
― How Not to Be Wrong: The Power of Mathematical Thinking
“I have known both of you all your lives, have carried your Daddy in my arms and on my shoulders, kissed and spanked him and watched him learn to walk. I don’t know if you’ve known anybody from that far back; if you’ve loved anybody that long, first as an infant, then as a child, then as a man, you gain a strange perspective on time and human pain and effort. Other people cannot see what I see whenever I look into your father’s face, for behind your father’s face as it is today are all those other faces which were his. Let him laugh and I see a cellar your father does not remember and a house he does not remember and I hear in his present laughter his laughter as a child. Let him curse and I remember him falling down the cellar steps, and howling, and I remember, with pain, his tears, which my hand or your grandmother’s so easily wiped away. But no one’s hand can wipe away those tears he sheds invisibly today, which one hears in his laughter and in his speech and in his songs.”
― The Fire Next Time
― The Fire Next Time
“Grothendieck transformed modern mathematics. However, much of the credit for this transformation should go to a lesser-known forerunner of his, Emmy Noether. It was Noether, born in Bavaria in 1882, who largely created the abstract approach that inspired category theory.1 Yet as a woman in a male academic world, she was barred from holding a professorship in Göttingen, and the classicists and historians on the faculty even tried to block her from giving unpaid lectures—leading David Hilbert, the dean of German mathematics, to comment, “I see no reason why her sex should be an impediment to her appointment. After all, we are a university, not a bathhouse.” Noether, who was Jewish, fled to the United States when the Nazis took power, teaching at Bryn Mawr until her death from a sudden infection in 1935.”
― When Einstein Walked with Gödel: Excursions to the Edge of Thought
― When Einstein Walked with Gödel: Excursions to the Edge of Thought
“In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of thirty or thirty-five years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone.”
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Crimson Reads
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— last activity Jan 11, 2014 08:15PM
A casual reading club for Harvard's Class of 2018 to while away their time being semi-intellectual. If you are new to goodreads, and want to edit how ...more
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