Many of the successes of `fancy' mathematics are due to sociological and linguistic reasons. They are really high-school-algebra arguments in disguise. Once you strip the fancy verbiage off, what remains is a bare (and much prettier, in my eyes) argument in high-school mathematics, or at most, in Freshman linear-algebra and (formal!) Calculus. For example, I am (almost) sure that Wiles's proof would be expressible in simple language, and if not, there would be a much nicer proof that would.
Doron ZeilbergerRelated topics
almost argument bare calculus disguise due example fancy formal freshman language mathematics off once pretty proof simple strip sure remains eyesRelated quotes
I was all for setting up a separate Jewish state in Madagascar or Palestine or someplace, but not to exterminate them. Besides, by exterminating 4 million Jews - they say 5 or 6 million at this trial, but that is all propaganda, I am sure it wasn't more than 4.5 million - they have made martyrs out of those Jews. For example, because of the extermination of these Jews, anti-Semitism has been set back many years in certain foreign countries where it had been making good progress.
Julius Streicher
Spinoza, for example, thought that insight into the essence of reality, into the harmonious structure of the eternal universe, necessarily awakens love for this universe. For him, ethical conduct is entirely determined by such insight into nature, just as our devotion to a person may be determined by insight into his greatness or genius. Fears and petty passions, alien to the great love of the universe, which is logos itself, will vanish, according to Spinoza, once our understanding of reality is deep enough.
Max Horkheimer
The book, as it stands, seems to me to be one of the most frightful muddles I have ever read, with scarcely a sound proposition in it beginning with page 45 [Hayek provided historical background up to page 45; after that came his theoretical model], and yet it remains a book of some interest, which is likely to leave its mark on the mind of the reader. It is an extraordinary example of how, starting with a mistake, a remorseless logician can end up in bedlam.
John Maynard Keynes
Character in many ways is everything in leadership. It is made up of many things, but I would say character is really integrity. When you delegate something to a subordinate, for example, it is absolutely your responsibility, and he must understand this. You as a leader must take complete responsibility for what the subordinate does. I once said, as a sort of wisecrack, that leadership consists of nothing but taking responsibility for everything that goes wrong and giving your subordinates credit for everything that goes well.
Dwight D. Eisenhower
The elephant, not only the largest but the most intelligent of animals, provides us with an excellent example. It is faithful and tenderly loving to the female of its choice, mating only every third year and then for no more than five days, and so secretly as never to be seen, until, on the sixth day, it appears and goes at once to wash its whole body in the river, unwilling to return to the herd until thus purified. Such good and modest habits are an example to husband and wife.
Francis de Sales