A Quote by Georg C. Lichtenberg
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.
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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.
Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.
Parenting forces us to get to know ourselves better than we ever might have imagined we could--and in many new ways. . . . We'll discover talents we never dreamed we had and fervently wish for others at moments we feel we desperately need them. As time goes on, we'll probably discover that we have more to give and can give more than we ever imagined. But we'll also find that there are limits to our giving, and that may be hard for us to accept.
New directions in science are launched by new tools much more often than by new concepts. The effect of a concept-driven revolution is to explain old things in new ways. The effect of a tool-driven revolution is to discover new things that have to be explained.
To invent without scruple a new principle to every new phenomenon, instead of adapting it to the old; to overload our hypothesis with a variety of this kind, are certain proofs that none of these principles is the just one, and that we only desire, by a number of falsehoods, to cover our ignorance of the truth.
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.
For too long we've been told about 'us' and 'them.' Each and every election we see a new slate of arguments and ads telling us that 'they' are the problem, not 'us.' But there can be no 'them' in America. There's only us.
Believers who have formulated such proofs [for God's existence] ... would never have come to believe as a result of such proofs
Challenges are gifts that force us to search for a new center of gravity. Don't fight them. Just find a new way to stand.
We can scarcely indeed look into any part of the sacred volume without meeting abundant proofs, that it is the religion of the Affections which God particularly requires. Love, Zeal, Gratitude, Joy, Hope, Trust, are each of them specified; and are not allowed to us as weaknesses, but enjoined on us as our bounden duty, and commended to us as our acceptable worship.
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.
Grieving is a journey that teaches us how to love in a new way now that our loved one is no longer with us. Consciously remembering those who have died is the key that opens the hearts, that allows us to love them in new ways.
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
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.
Dear to us are those who love us... but dearer are those who reject us as unworthy, for they add another life; they build a heaven before us whereof we had not dreamed, and thereby supply to us new powers out of the recesses of the spirit, and urge us to new and unattempted performances.
The Americans say that we are ungrateful-but I ask them for heaven's sake, what should we be grateful to them for-for murdering our fathers and mothers?-Or do they wish us to return thanks to them for chaining and handcuffing us, branding us, cramming fire down our throats, or for keeping us in slavery, and beating us nearly or quite to death to make us work in ignorance and miseries, to support them and their families. They certainly think we are a gang of fools.
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