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“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. I know what the world has done to my brother and how narrowly he has survived it. And I know, which is much worse, and this is the crime of which I accuse my country and my countrymen, and for which neither I nor time nor history will ever forgive them, that they have destroyed and are destroying hundreds of thousands of lives and do not know it and do not want to know it.”
― The Fire Next Time
― The Fire Next Time
“Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.”
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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
“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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“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
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