A Quote by David Berlinski
An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up.
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An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.
A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.
I'm pretty laidback as a dad anyway. I just trust her so much. She has a great head on her shoulders and she makes pretty good decisions most of the time. She even has enough common sense that if she makes a bad one she makes adjustments and knows that's what life is. It's a day-by-day, step-by-step journey through life, as she says in the movie.
Asked for a testimony to the effect that Emmy Noether was a great woman mathematician, he said: I can testify that she is a great mathematician, but that she is a woman, I cannot swear.
The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth.
She's my friend, the boy said simply. That's who she is and that's enough for me. As Minli looked at the buffalo boy, aglow with happiness against his poor surroundings, she saw it was enough for him. More than enough, as the smile that kept curling up on his face told her.
I did not know that the first step in any domestic violence relationship is to seduce and charm the victim. I also did not know that the second step is to isolate the victim. The next step in the domestic violence pattern is to introduce the threat of violence and see how she reacts. We victims know something you [non-victims] usually don't. It's incredibly dangerous to leave an abuser, because the final step in the domestic violence pattern is to 'kill her'. Over 70% of domestic violence murders happens after the victim has ended the relationship.
I focused on where she was from of course, her voice and her history, her relationship with God - her religion. This was probably the strongest relationship she has had, really. She never seemed to maintain close relationships with husbands.
Sure, I’m sad, but I’m not looking to soothe that sadness by replacing it with a new relationship. Women are allowed to be sad, and they’re allowed to be single, and they don’t need to hear that one day a man is going to make it all go away by telling her she is good enough again. She’s good enough as she is.
The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not...
Sufficiency isn't two steps up from poverty or one step short of abundance. It isn't a measure of barely enough or more than enough. Sufficiency isn't an amount at all. It is an experience, a context we generate, a declaration, a knowing that there is enough, and that we are enough.
Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly-yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
She is so naked and singular. She is the sum of yourself and your dream. Climb her like a monument, step after step. She is solid.
When she reached the shallow end, Kingsley held out his hand and pulled her up, but she lost her step and fell into his arms, her body crushing momentarily against his.
She'd assumed she'd be married and have kids by this age, that she would be grooming her own daughter for this, as her friends were doing. She wanted it so much she would dream about it sometimes, and then she would wake up with the skin at her wrists and neck red from the scratchy lace of the wedding gown she'd dreamed of wearing. But she'd never felt anything for the men she'd dated, nothing beyond her own desperation. And her desire to marry wasn't strong enough, would never be strong enough, to allow her to marry a man she didn't love.
If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.
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