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.
The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it. And though there be a greater number and weight of instances to be found on the other side, yet these it either neglects and despises, or else by some distinction sets aside and rejects, in order that by this great and pernicious predetermination the authority of its former conclusions may remain inviolate.
Not all, nor even a majority, are saved. . . They are indeed many, if regarded by themselves, but they are few in comparison with the far larger number of those who shall be punished with the devil.
The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language.
These cruel, wanton, indiscriminate bombings of London are, of course, a part of Hitler's invasion plans. He hopes, by killing large numbers of civilians, and women and children, that he will terrorise and cow the people of this mighty imperial city ... Little does he know the spirit of the British nation, or the tough fibre of the Londoners.
You propound a complicated arithmetical problem: say cubing a number containing four digits. Give me a slate and half an hour's time, and I can produce a wrong answer.
Once you've learned to think you can't stop. And an enormous number of people devote their lives to keeping their minds busy and feel extremely uncomfortable with silence.
The day is made up of 24 hours and an infinite number of moments. We need to be aware of those moments and make the most of them regardless of whether we're busy doing something or contemplating life.
But obviously a state which becomes progressively more and more of a unity will cease to be a state at all. Plurality of numbers is natural in a state; and the farther it moves away from plurality towards unity, the less of a state it becomes and the more a household, and the household in turn an individual.
If torture is going to be administered as a last resort in the ticking-bomb case, to save enormous numbers of lives, it ought to be done openly, with accountability, with approval by the president of the United States or by a Supreme Court justice.