Facts are not truths; they are not conclusions; they are not even premises, but in the nature and parts of premises.
I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions - they are not just repetitions of each other.
It is the facts that matter, not the proofs. Physics can progress without the proofs, but we can't go on without the facts ... if the facts are right, then the proofs are a matter of playing around with the algebra correctly.
All political debates, from tax policy to abortion, draw on moral arguments that rest on religious premises.
Believers who have formulated such proofs [for God's existence] ... would never have come to believe as a result of such proofs
How it chanced that a man who reasoned on his premises so ably, should assume his premises so foolishly, is one of the great mysteries of human nature.
Mathematicians are proud of the fact that, generally, they do their work with a piece of chalk and a blackboard. They value hand-done proofs above all else. A big question in mathematics today is whether or not computational proofs are legitimate. Some mathematicians won't accept computational proofs and insist that a real proof must be done by the human hand and mind, using equations.
We exist, and are quoted, as standing proofs that a government, so modeled as to rest continually on the will of the whole society, is a practicable government.
A sane man often reasons from sound premises; an insane man commonly reasons as well, but the premises are unsound.
What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.
The most painstaking phase comes when the manuscript is set in 'type' for the first time and the first proofs of the book are printed. These initial copies are called first-pass proofs or galleys.
I'm a bitter-ender. It's potentially my fatal flaw that I do not give up on something. I will not rest. I work and work and work until I can no longer and someone has to remove me from the premises.
Women never reason, or, if they do, they either draw correct inferences from wrong premises, or wrong inferences from correct premises; and they always poke the fire from the top.
Those who have racked their brains to discover new proofs have perhaps been induced to do so by a compulsion they could not quite explain to themselves. Instead of giving us their new proofs they should have explained to us the motivation that constrained them to search for them.
Rest, rest, rest, rest, rest. Nutrition is obviously very important, but rest is equally important. At rest is when your body is trying to recover.
The establishment of formal standards for proofs about programs... and the proposal that the semantics of a programming language may be defined independently of all processors for that language, by establishing standards of rigor for proofs about programs in the language, appears to be novel.