Erdos Quotes

[When asked why are numbers beautiful?] It’s like asking why is Ludwig van Beethoven’s Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.

I'll tell you once, and I'll tell you again. There's always a prime between n and 2n.

A mathematician is a device for turning coffee into theorems

Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper

When Euler died, he simply said I am finished and collapsed, to which someone in the audience muttered darkly" Another conjecture of Euler is proved

Non numerantur, sed ponderantur

The different religions confused me. Which was the right one? I tried to figure it out but had no success. It worried me. The different Gods - Catholic, Jewish, Protestant, Mohammedan - seemed very particular in the way in which they expected me to keep on good terms with them. I couldn't please one without offending the others. One kind soul solved my problem by taking me on my first trip to the planetarium. I contemplated the insignificant flyspeck called Earth, the millions of suns and solar systems, and concluded that whoever was in charge of all this would not throw a fit if I ate ham, or meat on Friday, or did not fast in the daytime during Ramadan. I felt much better after this and was, for a while, keenly interested in astronomy.

Speak the speech, I pray you, as I pronounced it to you, trippingly on the tongue. But if you mouth it, as many of our players do, I had as lief the town crier spoke my lines. Nor do not saw the air too much with your hand, thus, by use all gently, for in the very torrent, tempest, and (as I may say) whirlwind of your passion, you must acquire and beget a temperance that may give it smoothness. O, it offends me to the soul to hear a robustious periwig-pated fellow tear a passion to tatters, to very rags, to split the ears of the groundlings, who for the most part are capable of nothing but inexplicable dumb shows and noise. I would have such a fellow whipped for o'erdoing Termagant. It out-herods Herod. Pray you avoid it. Be not too tame neither, but let your own discretion be your tutor. Suit the action to the word, the word to the action, with this special observance, that you o'erstep not the modesty of nature. For anything so overdone is from the purpose of playing, whose end, both at the first and now, was and is, to hold, as 'twere, the mirror up to nature, to show virtue her own feature, scorn her own image, and the very age and body of the time his form and pressure. Now this overdone, or come tardy off, though it make the unskillful laugh, cannot but make the judicious grieve, the censure of the which one must in your allowance o'erweigh a whole theatre of others. O, there be players that I have seen play, and heard others praise, and that highly (not to speak profanely), that neither having th' accent of Christians, nor the gait of Christian, pagan, nor man, have so strutted and bellowed that I have thought some of Nature's journeymen had made men, and not made them well, they imitated humanity so abominably. Reform it altogether! And let those that play your clowns speak no more than is set down for them, for there be of them that will themselves laugh, to set on some quantity of barren spectators to laugh too, though in the mean time some necessary question of the play be then to be considered. That's villainous and shows a most pitiful ambition in the fool that uses it. Go make you ready.

I think it was a sense of being completely swallowed up by nature that gave the prairie its powerful attraction.There is nothing like it in all of Europe. Even high up on a Swiss glacier one is still conscious of the toy villages below, the carefully groomed landscape of multicolored fields,the faraway ringing of a church bell. It is all very beautiful, but it does not convey the utmost escape. I believe, with the Indians, that a landscape influences and forms the people living on it and that one cannot understand them and make friends with them without also understanding, and making friends with, the earth from which they came.

There is an old debate," Erdos liked to say, "about whether you create mathematics or just discover it. In other words, are the truths already there, even if we don't yet know them?" Erdos had a clear answer to this question: Mathematical truths are there among the list of absolute truths, and we just rediscover them. Random graph theory, so elegant and simple, seemed to him to belong to the eternal truths. Yet today we know that random networks played little role in assembling our universe. Instead, nature resorted to a few fundamental laws, which will be revealed in the coming chapters. Erdos himself created mathematical truths and an alternative view of our world by developing random graph theory. Not privy to nature's laws in creating the brain and society, Erdos hazarded his best guess in assuming that God enjoys playing dice. His friend Albert Einstein, at Princeton, was convinced of the opposite: "God does not play dice with the universe.

A tremendous thunderclap was heard, the loudest there has ever been ... The sun remained hidden behind dark clouds, and there was only twilight, gray and misty. Then the earth trembled, and there came a great roar of something immense moving. The people saw a sheer green wall advancing toward them, filling the valley from one side to the other. At first they did not know what it was, and then they realized that it was a wall of green water. Destroying everything in its path, it came like a huge beast, a green monster, rushing upon them, foaming, hissing, in a cloud of spray. It engulfed the seer's house and carried it away with the seer, who was never seen again. Then the water fell upon the villages, sweeping away homes, people, fields and trees. The flood swept the valley clean as with a broom. Then it rushed on beyond the valley to wreak havoc elsewhere.

When the interests of Erdos's colleagues drifted away from pure mathematics, he made no secret of his disapproval. "When I wasn't sure whether to stay a mathematician or go to the Technical University and become an engineer, Vazsonyi recalled, "Erdos warned me: 'I'll hide, and when you enter the Technical University, I will shoot you.' That settled the matter." When probability theorist Mark Kac had a paper published in the Journal if Applied Physics based on his work during the war at MIT's Radiation Laboratory, Erdos sent him a one sentence postcard: "I am praying for your soul." Erdos was "reminding me," Kac said, "that I might be straying from the path of true virtue, which, as a matter of fact, I was.

The discovery that on the Web a few hubs grab most of the links initiated a frantic search for hubs in many areas. The results are startling: We now know that Hollywood, the Web, and society are not unique by any means. For example, hubs surface in the cell, in the network of molecules connected by chemical reactions. A few molecules, such as water or ademosine triphosphate (ATP), are the Rod Steigers of the cell, participating in a huge number of reactions. On the Internet, the network of physical lines connecting computers worldwide, a few hubs were determined to play a crucial role in guaranteeing the Internet's robustness against failures. Erdos is a major hub of mathematics, as 507 mathematicians have Erdos number one. According to an AT&T study, a few phone numbers are responsible for an extraordinarily high fraction of calls placed or received. While those with a teenager living in their homes might have suspicions about the identity of some of these phone hubs, the truth is that telemarketing firms and consumer service numbers are probably the real culprits. Hubs appear in most large complex networks that scientists have been able to study so far. They are ubiquitous, a generic building block of our complex, interconnected world.

This unique and deep meaning of power laws perhaps explains our excitement when we first spotted them on the Web. It wasn't only that they were unprecedented and unexpected in the context of networks. It was that they lifted complex networks out of the jungle of randomness where Erdos and Renyi had placed them forty years earlier and dropped them into the center of the colorful and conceptually rich arena of self-organization. Gazing at the power laws that our little search engine carried home from its journey, we caught a glimpse of a new and unsuspected order within networks, one that displayed an uncommon beauty and coherence.

Elderly Cheyenne warriors, weary of the misery and boredom of old age, made elaborate preparations to end their lives in battle. Yet accepting death was also an affirmation of life, for Crazy Horse also said he could die willingly because all the things he held dear—the sun, the land, the buffalo—were close by; his willingness to die was part of his way of honoring the human spirit. It was the lot of all people. As Sioux warriors acknowledged, "Only the rocks and mountains last forever; men must die.