Proofs Quotes
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All proofs rest on premises.
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The Prussian Academy of Sciences is a fast-track academic institute that requires a proactive, hands-on-type individual to overthrow the Newtonian conception of the universe. The successful candidate will have an excellent command of mass, energy, space, time and some maths. Bonus paid upon completion of proofs.
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Now all orators effect their demonstrative proofs by allegation either of enthymems or examples, and, besides these, in no other way whatever.
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Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.
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The art of drawing conclusions from experiments and observations consists in evaluating probabilities and in estimating whether they are sufficiently great or numerous enough to constitute proofs. This kind of calculation is more complicated and more difficult than it is commonly thought to be. . . .
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It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.
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It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.
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There is no tongue to speak his eulogy; Too brightly burned his splendour for our eyes: Far easier to condemn his injurers, Than for the tongue to reach his smallest worth. He to the realms of sinfulness came down, To teach mankind; ascending then to God, Heaven unbarred to him her lofty gates, To whom his country hers refused to ope. Ungrateful land, to its own injury Nurse of his fate! Well too does this instruct, That greatest ills fall to the perfectest. And 'midst a thousand proofs, let this suffice, That, as his exile had no parallel, So never was there man more great than he.
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I find OOP methodologically wrong. It starts with classes. It is as if mathematicians would start with axioms. You do not start with axioms - you start with proofs. Only when you have found a bunch of related proofs, can you come up with axioms. You end with axioms. The same thing is true in programming: you have to start with interesting algorithms. Only when you understand them well, can you come up with an interface that will let them work.
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A mathematician's reputation rests on the number of bad proofs he has given.
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Good works are the seals and proofs of faith; for even as a letter must have a seal to strengthen the same, even so faith must have good works.
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Living by the wisdom of computer science doesn’t sound so bad after all. And unlike most advice, it’s backed up by proofs.
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I think it's really fascinating that geometry is so difficult. My guess is it's difficult because it focuses on proofs.
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Let us hear the suspicions. I will look after the proofs.
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"There is no deception now, Mr. Weller. Tears," said Job, with a look of momentary slyness, "tears are not the only proofs of distress, nor the best ones."
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If only I had the Theorems! Then I should find the proofs easily enough.
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...a statement from you is more convincing than all the proofs in the world.
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Computer assisted proofs are getting better and better and computers will play a bigger and bigger role in the future.
