Mathematicians From England

"And now I think about it, I never really wanted to live forever. I just want to live well."

"But humans had to learn to ignore appearance. No two beings who shared common thinking processes and common goals should be truly alien to each other."

"“I’ve been testing Kallen’s Law—my name for it, not his. Remember what he said? ‘Anything that can be put into a data bank by one person can be taken out of it by another, if you’re smart enough and have enough time.’ That’s one problem with a computer-based society, and one reason why computers were so tightly controlled on Pentecost: it’s almost impossible to prevent access to computer-stored information.”"

"Although the schoolchildren of this country emerge from our institutions of supposed learning ninety percent illiterate, knowing nothing of science, nothing of technology, little geography, and less history, every one of them will tell you who rules the country. We are governed by the interaction of a President, learned judges, and our people’s representatives. Every child knows this; and every child is wrong. Perhaps it was once that way, but today the Court and President and Congress are either members of the old and wealthiest families, like the Michelsons and Brooks; or they have been bought and controlled by them. The sprawl of government passes and implements policies. But far fewer people, about a hundred in number, set policies."

"Where orbits are wildly varying, life has no chance to develop. Changes are too extreme. Temperatures melt tin, then solidify nitrogen. If it is once established, life is persistent; it can adapt to many extremes. But there is a fragility in the original creation that calls for a long period of tightly-controlled variations."

"But mere plausibility did not make the statement true."

"“It is my personal belief that nothing can exceed light speed,” said Sy at last. “I will mistrust anyone, government or Immortal, man or woman, human or alien, who attempts to tell me otherwise without providing convincing evidence.”"

"The heirs, naturally, wanted everything to be theirs as soon as possible. No one is more rapacious, ruthless, and impatient than a loving family member."

"No purpose is served by making private suffering into a public event."

"See, everybody looks at the world from his own point of view. I call it the ground state of the resting mind. And your brain does the same thing, left alone it returns to and thinks about what it’s really interested in."

"“It sounds reasonable to me.” “Reasonable, but not true. Big difference.”"

"“Could it wipe out life on Earth?” “Oh, I very much doubt that. Single-celled and oceanic forms will presumably survive. But it might make life impossible for humans.” “Actually, that tends to be my primary concern. Sponges and oysters will have to take care of themselves.”"

"“Lop the top-end tail off the distribution of human intelligence and creativity,” he went on, “and it would make no measurable difference to the population. Only one person in a billion is out beyond the six-sigma level. That’s what we’re talking about here. But eventually those one-in-a-billion make a huge difference. Ninety-five percent of all human progress comes from less than one thousandth of one percent of the population.”"

"Sometimes wealth and power merely created the desire for more of the same."

"When you got right down to it, every important decision in life was made with inadequate information."

"TIG. Trust In Government. An old political principle, to give your organization a name that’s the opposite of what you mean."

"Not it. He. Bey was sure he would have determined that for himself after a few more seconds. There were a hundred clues as to the innate sex of a form, and most of them had nothing to do with appearance or dress."

"Earth has been regarded for centuries as a giant self-regulating machine, absorbing all changes, great and small, and diluting their effects until they become invisible on a global scale. Mankind has taken that stability for granted. Careless of consequences, we have watched as forests were cleared, lakes poisoned, rivers dammed and diverted, mountains leveled, whole plains dug out for their mineral and fuel content. And nothing disastrous happened. Earth tolerated the insults, and always she restored the status quo. Always—until now. Until finally some hidden critical point has been passed. The move away from a steady state is signalled in many ways: by increasing ocean temperatures, by drought and flood, by widespread loss of topsoil, by massive crop failure, and by the collapse of worldwide fishing industries."

"Intelligence is too subtle an attribute to be inferred from appearance."

"Human history extends for approximately ten thousand years before the Expansion, with written records available for roughly half that time. Unfortunately, the human tendency for self-delusion, self-aggrandizement, and baseless faith in human superiority over all other intelligent life-forms renders much of the written record unreliable. Serious research workers are advised to seek alternative primary data sources concerning humans. —From the Universal Species Catalog (Subclass: Sapients)"

"He realized a profound truth: there is no one so generous as a bureaucrat spending other people’s money."

"When you pay somebody off, it only increases their demands. I know, only too well. They are never satisfied with what they get."

"Who should run the world? There’s no easy answer, no magic solution. There never is, to a really hard question."

"Sometimes I think about dying. And then I wonder about going to hell. And then I think that if and when I go there, the place will be completely organized and run by lost souls, with a council and a works committee and an ethics panel, and I’ll feel right at home."

"He had defined intuition for Sondra: it was what remained after all the facts had been forgotten. But intuition could also be something else. Sometimes it was the subconscious mind, establishing deep connections long before the thinking part of the brain could explain them."

"“My aunt doesn’t even believe there is a Ship. She says we’ve been here on Pentecost forever.” “What did you tell her?” “Nothing. For someone with that view, logic is irrelevant—she’ll believe what she chooses, regardless of evidence. Her religion says God placed us here on Pentecost, and for her that’s the end of the argument.” “And you?” Peron was aware that she had moved in very close to him. “What do you think?” “You know what I think. I’m cursed with a logical mind, and a lot of curiosity.”"

"Life’s not chess, and life’s not poker, but there’s some of both in it."

"One form of insanity bears the name curiosity."

"The superior strain of peas is the one whose genetic composition allows it to adapt to whatever environment it is presented with. People are not peas, but in one respect they are not very different from them: some have superior genetic composition to others."

"... the dialogue between mathematical physics, geometry, and algebraic topology. The interaction between these subjects has been such a dominant feature of research developments in the past few years that it seems scarcely necessary to recite a list of examples: in fact, on the mathematical side it is quite hard to think of active areas in geometry and topology which have not been noticeably influenced by insights from physics—where by "physics" we mean particularly quantum field theory—and on the other hand the geometrisation of fundamental physical concepts is a profound and pervasive development."

"Geometers have studied the topology of closed surfaces and their higher- dimensional analogues (manifolds) for a long time. But a remarkable breakthrough came in the early 1980s when Simon Donaldson found some totally new and unexpected invariants of four-dimensional manifolds. These were based on the Yang–Mills equations of physics but it was not until later that Edward Witten again showed how to interpret Donaldson's invariants in terms of quantum field theory. Later still, using duality ideas from string theory, Witten and Seiberg made a significant improvement of Donaldson theory which led to solutions of old problems."

"Chapter 10, p. 429"

"Chapter 1, p. 22"

"Chapter 1, p. 27"

"Chapter 2, p. 30"

"Chapter 10, p. 313"

"(quote from p. 62)"

"Chapter 10, p. 338 (remark translated from H. A. Schwarz's Formeln und Lehrsätze zum Gebrauche der elliptischen Funktionen)"

"Introduction, p. ix"

"Chapter 1, p. 1"

"Mathematicians are extremely lucky, they are paid for doing what they would by nature have to do anyway. One should not have a non-teaching fellowship too long, there comes a time when one must make a contribution to society. Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem."

"Conway made a fortuitous match for a Ph.D. adviser in Harold Davenport, considered the leader of the internationally respected British school of number theory. And while politically and socially speaking Conway was a radical, Davenport was a conservative. “All changes are for the worse,” he'd say. And looking back upon his career and his charges, he said: “I had 2 very good students. Baker”—Alan Baker, later a Fields Medalist—“to whom I would give a problem and he would return with a very good solution. And Conway, to whom I would give a problem and he would return with a very good solution to another problem.”"

"[T]his work... is intended fundamentally as a permanent memorial to the Founder of the , and embraces material which may easily perish or be ultimately lost sight of. ...My object is... to issue a volume to some extent worthy of the name of the man it bears,—which may be studied hereafter by those who wish to understand him, his origin and his aims..."

"[T]his work is not written to gain a public, but piam memoriam prodere conditoris nostri and is intended especially for those who have known and loved Francis Galton in the past, or who may in the future desire to understand and honour him."

"Those who know the real history of the one occasion on which Galton and Darwin disagreed know how loyal Galton was to Darwin—loyal with a loyalty far rarer to-day. Galton would not have wished me to put him in the same rank as his master, but the reader who follows my story to the end may possibly see that the ramifications of Galton's methods are producing a renascence in innumerable branches of science..."

"[I]t was soon clear to me that I was collecting as much information bearing on the family history of Charles Darwin as on that of Francis Galton. It seemed desirable to place the two men to some extent in contrast in my volume, showing in ancestry, in methods of work and in outlook on life what they had in common and how they differed."

"The statistician Karl Pearson analyzed a large number of outcomes at certain roulette tables and suggested that the wheels were biased. He wrote in 1894: Clearly, since the Casino does not serve the valuable end of huge laboratory for the preparation of probability statistics, it has no scientific raison d’être... [E]arly experiments were suggestive and led to important discoveries in probability and statistics. They led Pearson to the ', which is of great importance in testing whether observed data fit a given ."

"It was only the feeling that, at least in one or two aspects of Francis Galton's later life and of his scientific work, I could perhaps put his contributions to human knowledge more adequately than possibly one or another who might take up the task, if I resigned it, and who would hardly grasp the bearing of that long and intimate scientific correspondence between Galton, Weldon and myself, that I persevered in my endeavour to give some account of a life, wherein an important chapter of personal development must remain largely unrecorded."

"If my view be correct, Erasmus Darwin planted the seed of suggestion in questioning whether adaptation meant no more to man than illustration of creative ingenuity; the one grandson, Charles Darwin, collected the facts which had to be dealt with and linked them together by wide-reaching hypotheses; the other grandson, Francis Galton, provided the methods by which they could be tested..."

"[I]t is better to be content with the fraction of a right solution than to beguile ourselves with the whole of a wrong solution."