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 Middle East has gone through periods of turmoil before. In the 1950s and 1960s, there were revolutions. When monarchies were collapsing in a number of countries, we had radicals and we had Nasserism. Today it's a little bit more complicated.
I never said it. Honest. Oh, I said there are maybe 100 billion galaxies and 10 billion trillion stars. It's hard to talk about the Cosmos without using big numbers. I said "billion" many times on the Cosmos television series, which was seen by a great many people. But I never said "billions and billions." For one thing, it's too imprecise. How many billions are "billions and billions"? A few billion? Twenty billion? A hundred billion? "Billions and billions" is pretty vague. When we reconfigured and updated the series, I checked-and sure enough, I never said it.
Generally speaking, our prisoners were capable of loving animals, and if they had been allowed they would have delighted to rear large numbers of domestic animals and birds in the prison. And I wonder what other activity could better have softened and refined their harsh and brutal natures than this. But it was not allowed. Neither the regulations nor the nature of the prison made it possible.
Number one comes freedom first for my people and equality. And this is what I plan to do after I'm through fighting - working with nothing but the people, the little people in the alleys: the downtrodden people, going out and helping them with my image.
The secrets of evolution are death and time-the deaths of enormous numbers of lifeforms that were imperfectly adapted to the environment; and time for a long succession of small mutations.
In the 'in-itself' there is nothing of 'causal connections', of 'necessity', or of 'psychological non-freedom'; there the effect does not follow the cause, there is no rule or 'law'. It is we alone who have devised cause, sequence, for-each-other, relativity, constraint, number, law, freedom, motive, and purpose; and when we project and mix this symbol world into things as if it existed 'in itself', we act once more as we have always acted- mythologically.
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.
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.
Germany suffered most as a consequence of this Peace Treaty and the general insecurity which was bound to arise from it. The unemployment figure rose to a third of the number usually employed in the nation, which means, however, that by counting the families of the unemployed as well there were 26 million people in Germany out of a population of 65 millions faced by an absolutely hopeless future.
That which is common to the greatest number has the least care bestowed upon it. Every one thinks chiefly of his own, hardly at all of the common interest; and only when he is himself concerned as an individual. For besides other considerations, everybody is more inclined to neglect the duty which he expects another to fulfill.
Any man who tries to be good all the time is bound to come to ruin among the great number who are not good. Hence a prince who wants to keep his authority must learn how not to be good, and use that knowledge, or refrain from using it, as necessity requires.