Whereas a novice makes moves until he gets checkmated (proof), a Grand Master realizes 20 moves in advance that it’s futile to continue playing (conceptualizing).
I could only defend myself so much. It was my word against his. There was no evidence, nor was there any proof. My word meant very little.
It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof.
The ideas which now pass for brilliant innovations and advances are in fact mere revivals of ancient errors, and a further proof of the dictum that those who are ignorant of the past are condemned to repeat it.
With impressive proof on all sides of magnificent progress, no one can rightly deny the fundamental correctness of our economic system.
In a private room he showed me the first specimens of gold, that is he was not certain if it was gold or not, but he thought it might be; immediately I made the proof and found that it was gold.
There is abundant proof that the opening of our ports always tends to raise the price of foreign corn to the price in the English market, and not to sink the price of British corn to the price in the continental market.
[Pepper sends Stark a gift: an arc reactor in a case] Virginia 'Pepper' Potts: [inscription] "Proof that Tony Stark has a heart."
If leaders in the space program had at its beginning in the 1940s, pointed out the benefits to people on earth rather than emphasizing the search for proof of evolution in space, the program would have saved $100 billion in tax money and achieved gre...
But when, in the first setting out, he takes it for granted without proof, that distinctions found in the structure of all languages, have no foundation in nature; this surely is too fastidious a way of treating the common sense of mankind.
In the field of outdoor sports, the American boy is easily capable of devising his own amusements, and until some proof is adduced that baseball is not his invention, I protest against this systematic effort to rob him of his dues.
For one human being to love another; that is perhaps the most difficult of all our tasks, the ultimate, the last test and proof, the work for which all other work is but preparation.
Love need not speak volumes. It need not demand proof. It never has a happy ending - simply because it doesn't end as long as love is pure and true”.
Rather than campaigning to help women, feminists today are more likely to be picking fights on Twitter, or dressing up petty grievances as proof of rampant 'sexism'.
There is no being eloquent for atheism. In that exhausted receiver the mind cannot use its wings, - the clearest proof that it is out of its element.
There's no bigger pleasure for a person perhaps than to enjoy his own company and its proof is that everyone loves sleeping as that helps them to be of their own and alone.
It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years.
Life after love was possible. I was proof. Loss taught you about yourself, burrowed in the dark parts of your soul and ate you from the inside out.
But we [women] are only at the beginning [of revamping feminism]. And our strictures on each other prove this. Our enforcement of thinness, of non-sexuality, of 'good' feminism versus 'bad' feminism, are proofs of our being at the beginning, not the ...
Many [Tudor-era religious radicals] believed then, exactly as Christian fundamentalists do today, that they lived in the 'last days' before Armageddon and, again just as now, saw signs all around in the world that they took as certain proof that the ...
