Mathematicians From The United States

"Discovery in mathematics is not a matter of logic. It is rather the result of mysterious powers which no one understands, and in which unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty's sake and pulls it down to earth."

"In the late 1920s and early 1930s, Veblen carried out three extraordinary initiatives. He helped to create the original . He influenced ’s decision to locate the in Princeton rather than Newark. And he became a founding member of the , which brought hundreds of refugees to Princeton and other universities."

"The importance of the theory of s in physical problems is due to the fact that when coordinates are used to describe physical phenomena (e.g. those studied in geometry) it is usually the case that the coordinates are no part of the phenomena themselves. They are generally put into the description by the observer. Therefore it is desirable to have the description in such terms that when stated in terms of one coordinate system, it can be read off easily in terms of other systems. Such statements will employ invariants of one sort or another."

"In instituting the , the has recognized the dual character of mathematics. On the one hand, mathematics is one of the essential emanations of the human spirit,—a thing to be valued in and for itself, like art or poetry. made notable contributions to this side of mathematics in his work on and multiple algebras. On the other hand, mathematics is the handmaiden and the helper of the other sciences, both in their most abstract generalizations and in their most concrete applications in industry."

"The old truths still hold: without a sustaining civilization, no isolated collection of ships and humans can rebuild the core of technology."

"Within thirty years, we will have the technological means to create superhuman intelligence. Shortly after, the human era will be ended."

"The acceleration of technological progress has been the central feature of this century."

"We can solve many problems thousands of times faster than natural selection. Now, by creating the means to execute those simulations at much higher speeds, we are entering a regime as radically different from our human past as we humans are from the lower animals."

"I have argued above that we cannot prevent the Singularity, that its coming is an inevitable consequence of the humans' natural competitiveness and the possibilities inherent in technology. And yet … we are the initiators. Even the largest avalanche is triggered by small things. We have the freedom to establish initial conditions, make things happen in ways that are less inimical than others. Of course (as with starting avalanches), it may not be clear what the right guiding nudge really is..."

"The work that is truly productive is the domain of a steadily smaller and more elite fraction of humanity."

"Quit crossing your fingers, Wim; the only thing that’ll ever save you from is the respect of educated men."

"Wil wondered fleetingly if she might be psychopathic, and not merely young and naive."

"There may have been some time in the past when a group calling themselves astrologers could produce results. I don’t know, and the matter doesn’t interest me, for I live in the present. In our time the men working in the name of astrology are incapable of producing results, are conscious frauds."

"Even as my conscious mind concluded that we were under fire, I threw myself on the ground and flatten into the lowest profile possible. You’ve heard the bromide about combat making life more real. I don’t know about that, but it’s certainly true that when you are flat against the ground with your face in the dirt, the whole universe looks different."

"Our system is founded on the Concept of Chaos. The universe is basically a dark and Unhappy place—a place where evil and injustice and randomness rule. The ironic thing is that the very act of organization creates the potential for even greater ruin. Social organizations have a natural tendency to become monopolistic and inflexible. When they finally break down, it is a catastrophic debacle. So, we must except a great deal of disorder and violence in our lives if we are to avoid a complete blow up later."

"The closer a Citizen came to the centers of power, the more of a madhouse the universe became."

"She was obviously an idealist: that is, someone who can twist his every vice into self-righteous morality."

"Some dreams take a long time in dying. Some get a last minute reprieve…and that can be even worse."

"One of his many mottos was, “If you didn’t figure it out yourself, you don’t understand it.”"

"Every state religion he’d ever seen had a core of hypocrisy. That was why he’d been against bringing “Hrala” ashore—he knew the priests would never accept their theology suddenly incarnate."

"Principal Alcalde was into a long speech, about the fast-changing world and the need for Fairmont to revolutionize itself from semester to semester. At the same time they must never forget the central role of modern education, which was to teach the kids how to learn, how to pose questions, how to be adaptable—all without losing their moral compass."

"Over the last twenty years, the worldwide net had come to be a midden of bogus sites and recursive fraudulence…telling truth from fantasy was often the hardest thing about using the web."

"That was the old saying: Once your secret is outed anywhere, however briefly, it is outed forever. “Oh, I don’t know,” said Juan. “The way to cover a slip is to embellish it, hide it in all sorts of fake secrets.”"

"Did you ever think? Old-fashioned writing is the ultimate in context tagging. It’s passive, informative, and present exactly where you need it."

"How to explain? How to describe? Even the omniscient viewpoint quails."

"Poor humans; they will all die." "Poor us; we will not."

"The hours came to minutes, the minutes to seconds. And now each second was as long as all the time before."

"Peregrine Wickwrackrum was of two minds about evil: when enough rules get broken, sometimes there is good amid the carnage."

"The voice was gentle, like a scalpel petting the short hairs of your throat."

"Politics may come and go, but Greed goes on forever."

"He was guided by what he saw rather than by what he wanted to believe."

"Life is a green madness just now, trying to squeeze the last bit of warmth from the season."

"I say, let’s learn more and then speculate."

"Sometimes terror and pain are not the best levers; deception, when it works, is the most elegant and least expensive manipulation of all."

"If during the last thousand seconds you have received any High-Beyond-protocol packets from "Arbitration Arts," discard them at once. If they have been processed, then the processing site and all locally netted sites must be physically destroyed at once. We realize that this means the destruction of solar systems, but consider the alternative. You are under Transcendent attack."

"Hexapodia as the key insight... I haven’t had a chance to see the famous video from Straumli Realm, except as an evocation. (My only gateway onto the Net is very expensive.) Is it true that humans have six legs?"

"It was not called the Net of a Million Lies for nothing."

"We've watched the Homo Sapiens interest group since the first appearance of the Blight. Where is this "Earth" the humans claim to be from? "Half way around the galaxy," they say, and deep in the Slow Zone. Even their proximate origin, Nyjora, is conveniently in the Slowness. We see an alternative theory: Sometime, maybe further back than the last consistent archives, there was a battle between Powers. The blueprint for this "human race" was written, complete with communication interfaces. Long after the original contestants and their stories had vanished, this race happened to get in position where it could Transcend. And that Transcending was tailor-made, too, re-establishing the Power that had set the trap to begin with.We're not sure of the details, but a scenario such as this is inevitable. What we must do is also clear. Straumli Realm is at the heart of the Blight, obviously beyond all attack. But there are other human colonies. We ask the Net to help in identifying all of them. We ourselves are not a large civilization, but we would be happy to coordinate the information gathering, and the military action that is required to prevent the Blight's spread in the Middle Beyond. For nearly seventeen weeks, we've been calling for action. Had you listened in the beginning, a concerted strike might have been sufficient to destroy the Straumli Realm. Isn't the Fall of Relay enough to wake you up? Friends, if we act together we still have a chance.Death to vermin."

"Well, what do you know," Pham said. "Butterflies in jackboots."

"He claimed that nearby gun thunder cleared the mind—but most everybody else agreed it made you daft."

"Effective translation of natural languages comes awfully close to requiring a sentient translator program."

"All his life he had lived by the law. Often his job had been to stop acts of revenge....And now revenge was all that life had left for him."

"Sometimes the biggest disasters aren’t noticed at all—no one’s around to write horror stories."

"Over the last few weeks, some newsgroups have been full of tales of war and battle fleets, of billions dying in the clash of species. To all such—and those living more peaceably around them—we say look out on the universe. It does not care, and even with all our science there are some disasters that we can not avert. All evil and good is petty before Nature. Personally, we take comfort from this, that there is a universe to admire that cannot be twisted to villainy or good, but which simply is."

"The heart of manipulation is to empathize without being touched."

"“I have come to kill you.” The death’s heads shrugged. “You have come to try.”"

"If there be only hours, at least learn what there is time to learn."

"Peregrine Wickwrackscar was flying. A pilgrim with legends that went back almost a thousand years—and not one of them could come near to this!"

"They’re very good at reaching nonsense conclusions from insufficient information."

"Technical people don’t make good slaves. Without their wholehearted cooperation, things fall apart."