’Tis late; the astronomer in his lonely height
Exploring all the dark, descries from far
Orbs that like distant isles of splendor are,
And mornings whitening in the infinite.…
He summons one disheveled, wandering star,—
Return ten centuries hence on such a night.
That star will come. It dare not by one hour
Cheat science, or falsify her calculation;
Men will have passed, but watchful in the tower
Man shall remain in sleepless contemplation;
And should all men have perished there in turn,
Truth in their stead would watch that star’s return.

“Wu Li” was more than poetic. It was the best definition of physics that the conference would produce. It caught that certain something, that living quality that we were seeking to express in a book, that thing without which physics becomes sterile. “Wu” can mean either “matter” or “energy.” “Li” is a richly poetic word. It means “universal order” or “universal law.” It also means “organic patterns.” The grain in a panel of wood is Li. The organic pattern on the surface of a leaf is also Li, and so is the texture of a rose petal. In short, Wu Li, the Chinese word for physics, means “patterns of organic energy” (“matter/ energy” [Wu] + “universal order/organic patterns” [Li]). This is remarkable since it reflects a world view which the founders of western science (Galileo and Newton) simply did not comprehend, but toward which virtually every physical theory of import in the twentieth century is pointing!

[A contemporary study] predicted the loss of two-thirds of all tropical forests by the turn of the century. Hundreds of thousands of species will perish, and this reduction of 10 to 20 percent of the earth’s biota will occur in about half a human life span. … This reduction of the biological diversity of the planet is the most basic issue of our time.

[Heisenberg's seminal 1925 paper initiating quantum mechanics marked] one of the great jumps—perhaps the greatest—in the development of twentieth century physics.

[In 18th-century Britain] engineers for the most began as simple workmen, skilful and ambitious but usually illiterate and self-taught. They were either millwrights like Bramah, mechanics like Murdoch and George Stephenson, or smiths like Newcomen and Maudslay.

[My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who] devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.

[Richard Feynman] believed in the primacy of doubt, not as a blemish upon our ability to know but as the essence of knowing. The alternative to uncertainty is authority, against which science has fought for centuries.

[There was] in some of the intellectual leaders a great aspiration to demonstrate that the universe ran like a piece of clock-work, but this was was itself initially a religious aspiration. It was felt that there would be something defective in Creation itself—something not quite worthy of God—unless the whole system of the universe could be shown to be interlocking, so that it carried the pattern of reasonableness and orderliness. Kepler, inaugurating the scientist’s quest for a mechanistic universe in the seventeenth century, is significant here—his mysticism, his music of the spheres, his rational deity demand a system which has the beauty of a piece of mathematics.

[Thomas Henry] Huxley, I believe, was the greatest Englishman of the Nineteenth Century—perhaps the greatest Englishman of all time. When one thinks of him, one thinks inevitably of such men as Goethe and Aristotle. For in him there was that rich, incomparable blend of intelligence and character, of colossal knowledge and high adventurousness, of instinctive honesty and indomitable courage which appears in mankind only once in a blue moon. There have been far greater scientists, even in England, but there has never been a scientist who was a greater man.

[While in school, before university,] I, like almost all chemists I know, was also attracted by the smells and bangs that endowed chemistry with that slight but charismatic element of danger which is now banned from the classroom. I agree with those of us who feel that the wimpish chemistry training that schools are now forced to adopt is one possible reason that chemistry is no longer attracting as many talented and adventurous youngsters as it once did. If the decline in hands-on science education is not redressed, I doubt that we shall survive the 21st century.

[About Francis Baily] The history of the astronomy of the nineteenth century will be incomplete without a catalogue of his labours. He was one of the founders of the Astronomical Society, and his attention to its affairs was as accurate and minute as if it had been a firm of which he was the chief clerk, with expectation of being taken into partnership.

Discovery always carries an honorific connotation. It is the stamp of approval on a finding of lasting value. Many laws and theories have come and gone in the history of science, but they are not spoken of as discoveries. Kepler is said to have discovered the laws of planetary motion named after him, but no the many other 'laws' which he formulated. ... Theories are especially precarious, as this century profoundly testifies. World views can and do often change. Despite these difficulties, it is still true that to count as a discovery a finding must be of at least relatively permanent value, as shown by its inclusion in the generally accepted body of scientific knowledge.

Il n'y a qu'un demi-siècle, un orateur chrétien, se défiant des hommes de la science leur disait: 'Arrêtez-vous enfin, et ne creusez pas jusqu'aux enfers.' Aujourd'hui, Messieurs, rassurés sur l'inébranlable constance de notre foi, nous vous disons: creusez, creusez encore; plus vous descendrez, plus vous rapprocherez du grand mystère de l'impuissance de l'homme et de la vérité de la religion. Creusez donc, creusez toujours,mundum tradidit disputationibus eorum; et quand la science aura donné son dernier coup de marteau sur les fondements de la terre, vous pourrez à la lueur du feu qu'il fera jaillir, lire encore l'idée de Dieu et contempler l'empreinte de sa main.
Only a half-century ago, a Christian speaker, mistrustful of men of science told them: 'Stop finally, and do not dig to hell.' Today, gentlemen, reassured about the steadfastness of our unshakeable faith, we say: dig, dig again; the further down you, the closer you come to the great mystery of the impotence of man and truth of religion. So dig, always dig: and when science has stuck its final hammer blow on the bosom of the earth, you will be able to ignite a burst of light, read furthermore the mind of God and contemplate the imprint of His hand.

Natura non facit saltum or, Nature does not make leaps… If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).

A century ago astronomers, geologists, chemists, physicists, each had an island of his own, separate and distinct from that of every other student of Nature; the whole field of research was then an archipelago of unconnected units. To-day all the provinces of study have risen together to form a continent without either a ferry or a bridge.

A century ago, Darwin and his friends were thought to be dangerous atheists, but their heresy simply replaced a benevolent personal deity called God by a benevolent impersonal deity called Evolution. In their different ways Bishop Wilberforce and T.H. Huxley both believed in Fate.

A definition of what we mean by “probability”. … The German Dictionary by Jakob and Wilhelm Grimm gives us detailed information: The Latin term “probabilis”, we are told, was at one time translated by “like truth”, or, by “with an appearance of truth” (“mit einem Schein der Wahrheit”). Only since the middle of the seventeenth century has it been rendered by “wahrscheinlich” (lit. truth-resembling).

A great nation is any mob of people which produces at least one honest man a century.

A great swindle of our time is the assumption that science has made religion obsolete. All science has damaged is the story of Adam and Eve and the story of Jonah and the Whale. Everything else holds up pretty well, particularly lessons about fairness and gentleness. People who find those lessons irrelevant in the twentieth century are simply using science as an excuse for greed and harshness. Science has nothing to do with it, friends.

A man who has once looked with the archaeological eye will never see quite normally. He will be wounded by what other men call trifles. It is possible to refine the sense of time until an old shoe in the bunch grass or a pile of nineteenth century beer bottles in an abandoned mining town tolls in one’s head like a hall clock.

A small bubble of air remained unabsorbed... if there is any part of the phlogisticated air [nitrogen] of our atmosphere which differs from the rest, and cannot be reduced to nitrous acid, we may safely conclude that it is not more than 1/120 part of the whole.
Cavendish did not realize the significance of the remaining small bubble. Not until a century later were the air’s Noble Gases appreciated.

Alcoholism, the opium habit and tobaccoism are a trio of poison habits which have been weighty handicaps to human progress during the last three centuries. In the United States, the subtle spell of opium has been broken by restrictive legislation; the grip of the rum demon has been loosened by the Prohibition Amendment to the Constitution, but the tobacco habit still maintains its strangle-hold and more than one hundred million victims of tobaccoism daily burn incense to the smoke god.

Almost every major systematic error which has deluded men for thousands of years relied on practical experience. Horoscopes, incantations, oracles, magic, witchcraft, the cures of witch doctors and of medical practitioners before the advent of modern medicine, were all firmly established through the centuries in the eyes of the public by their supposed practical successes. The scientific method was devised precisely for the purpose of elucidating the nature of things under more carefully controlled conditions and by more rigorous criteria than are present in the situations created by practical problems.

Almost everything that distinguishes the modern world from earlier centuries is attributable to science, which achieved its most spectacular triumphs in the seventeenth century.

Almost everything, which the mathematics of our century has brought forth in the way of original scientific ideas, attaches to the name of Gauss.

Although few expressions are more commonly used in writing about science than “science revolution,” there is a continuing debate as to the propriety of applying the concept and term “revolution” to scientific change. There is, furthermore, a wide difference of opinion as to what may constitute a revolution. And although almost all historians would agree that a genuine alteration of an exceptionally radical nature (the Scientific Revolution) occurred in the sciences at some time between the late fifteenth (or early sixteenth) century and the end of the seventeenth century, the question of exactly when this revolution occurred arouses as much scholarly disagreement as the cognate question of precisely what it was.

Although such research [into the paranormal] has yet to produce anything in the way of a repeatable controlled experiment, its practitioners argue that its revolutionary potentialities justify its continuation. My own feeling is that after a century of total failure it has become a bloody bore.

Animals, even plants, lie to each other all the time, and we could restrict the research to them, putting off the real truth about ourselves for the several centuries we need to catch our breath. What is it that enables certain flowers to resemble nubile insects, or opossums to play dead, or female fireflies to change the code of their flashes in order to attract, and then eat, males of a different species?

Arguably the greatest technological triumph of the century has been the public-health system, which is sophisticated preventive and investigative medicine organized around mostly low- and medium-tech equipment; ... fully half of us are alive today because of the improvements.

Arts and sciences in one and the same century have arrived at great perfection; and no wonder, since every age has a kind of universal genius, which inclines those that live in it to some particular studies; the work then, being pushed on by many hands, must go forward.

As a great man’s influence never ends, so also there is no definite finality, no end, to a great survey; it runs along for centuries, ever responsive to the strain of the increasing needs of a growing population and an enlarging domain.

As a progressive discipline [biochemistry] belongs to the present century. From the experimental physiologists of the last century it obtained a charter, and, from a few pioneers of its own, a promise of success; but for the furtherance of its essential aim that century left it but a small inheritance of facts and methods. By its essential or ultimate aim I myself mean an adequate and acceptable description of molecular dynamics in living cells and tissues.

As the Director of the Theoretical Division of Los Alamos, I participated at the most senior level in the World War II Manhattan Project that produced the first atomic weapons.
Now, at age 88, I am one of the few remaining such senior persons alive. Looking back at the half century since that time, I feel the most intense relief that these weapons have not been used since World War II, mixed with the horror that tens of thousands of such weapons have been built since that time—one hundred times more than any of us at Los Alamos could ever have imagined.
Today we are rightly in an era of disarmament and dismantlement of nuclear weapons. But in some countries nuclear weapons development still continues. Whether and when the various Nations of the World can agree to stop this is uncertain. But individual scientists can still influence this process by withholding their skills.
Accordingly, I call on all scientists in all countries to cease and desist from work creating, developing, improving and manufacturing further nuclear weapons - and, for that matter, other weapons of potential mass destruction such as chemical and biological weapons.
[On the occasion of the 50th Anniversary of Hiroshima.]

At some future period, not very distant as measured by centuries, the civilised races of man will almost certainly exterminate, and replace the savage races throughout the world.

Bernard Bolzano dispelled the clouds that throughout all the foregone centuries had enveloped the notion of Infinitude in darkness, completely sheared the great term of its vagueness without shearing it of its strength, and thus rendered it forever available for the purposes of logical discourse.

BIRTH, n. The first and direst of all disasters. As to the nature of it there appears to be no uniformity. Castor and Pollux were born from the egg. Pallas came out of a skull. Galatea was once a block of stone. Peresilis, who wrote in the tenth century, avers that he grew up out of the ground where a priest had spilled holy water. It is known that Arimaxus was derived from a hole in the earth, made by a stroke of lightning. Leucomedon was the son of a cavern in Mount Etna, and I have myself seen a man come out of a wine cellar.

But if we are to control evolution we shall have to find out how to influence gene reproduction in a definite direction, just as organic chemists nowadays work for definite ends. Such a possibility is at present entirely beyond our grasp, but a century hence it may not be so.

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.

But of all environments, that produced by man’s complex technology is perhaps the most unstable and rickety. In its present form, our society is not two centuries old, and a few nuclear bombs will do it in.
To be sure, evolution works over long periods of time and two centuries is far from sufficient to breed Homo technikos… .
The destruction of our technological society in a fit of nuclear peevishness would become disastrous even if there were many millions of immediate survivors.
The environment toward which they were fitted would be gone, and Darwin’s demon would wipe them out remorselessly and without a backward glance.

By the 18th century science had been so successful in laying bare the laws of nature that many thought there was nothing left to discover. Immutable laws prescribed the motion of every particle in the universe, exactly and forever: the task of the scientist was to elucidate the implications of those laws for any particular phenomenon of interest. Chaos gave way to a clockwork world. But the world moved on ...Today even our clocks are not made of clockwork. ... With the advent of quantum mechanics, the clockwork world has become a lottery. Fundamental events, such as the decay of a radioactive atom, are held to be determined by chance, not law.

By the end of the next century, the “greenhouse effect” may increase temperatures worldwide to levels that have not been reached for at least 100,000 years. And the effects on sea level and on agriculture and other human activities are likely to be so profound that we should be planning for them now.

By the fruit one judges the tree; the tree of science grows exceedingly slowly; centuries elapse before one can pluck the ripe fruits; even today it is hardly possible for us to shell and appraise the kernel of the teachings that blossomed in the seventeenth century. He who sows cannot therefore judge the worth of the corn. He must have faith in the fruitfulness of the seed in order that he may follow untiringly his chosen furrow when he casts his ideas to the four winds of heaven.

By the mid-1950s manatees were already scarce, and monk seals, once common as far north as Galveston, were gone. By the end of the 20th century, up to 90 percent of the sharks, tuna, swordfish, marlins, groupers, turtles, whales, and many other large creatures that prospered in the Gulf for millions of years had been depleted by overfishing.

By the nineteenth century … new circumstances called for new conformity enforcers… The government locked you in a house of penitence—a penitentiary—where your feelings of remorse would theoretically pummel you without cease.

Chemistry is the study of material transformations. Yet a knowledge of the rate, or time dependence, of chemical change is of critical importance for the successful synthesis of new materials and for the utilization of the energy generated by a reaction. During the past century it has become clear that all macroscopic chemical processes consist of many elementary chemical reactions that are themselves simply a series of encounters between atomic or molecular species. In order to understand the time dependence of chemical reactions, chemical kineticists have traditionally focused on sorting out all of the elementary chemical reactions involved in a macroscopic chemical process and determining their respective rates.

Children are told that an apple fell on Isaac Newton’s head and he was led to state the law of gravity. This, of course, is pure foolishness. What Newton discovered was that any two particles in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This is not learned from a falling apple, but by observing quantities of data and developing a mathematical theory that can be verified by additional data. Data gathered by Galileo on falling bodies and by Johannes Kepler on motions of the planets were invaluable aids to Newton. Unfortunately, such false impressions about science are not universally outgrown like the Santa Claus myth, and some people who don’t study much science go to their graves thinking that the human race took until the mid-seventeenth century to notice that objects fall.

Considered in its entirety, psychoanalysis won’t do. It is an end product, moreover, like a dinosaur or a zeppelin, no better theory can ever be erected on its ruins, which will remain for ever one of the saddest and strangest of all landmarks in the history of twentieth century thought.

Contrary to popular parlance, Darwin didn't discover evolution. He uncovered one (most would say the) essential mechanism by which it operates: natural selection. Even then, his brainstorm was incomplete until the Modern Synthesis of the early/mid-20th century when (among other things) the complementary role of genetic heredity was fully realized. Thousands upon thousands of studies have followed, providing millions of data points that support this understanding of how life on Earth has come to be as it is.

Cosmology, for centuries consisting of speculation based on a minimum of observational evidence and a maximum of philosophical predilection, became in the twentieth century an observational science, its theories now subject to verification or refutation to a degree previously unimaginable.

Data is the sword of the 21st century, those who wield it well, the Samurai.

Do you remember what Darwin says about music? He claims that the power of producing and appreciating it existed among the human race long before the power of speech was arrived at. Perhaps that is why we are so subtly influenced by it. There are vague memories in our souls of those misty centuries when the world was in its childhood.

Does it seem all but incredible to you that intelligence should travel for two thousand miles, along those slender copper lines, far down in the all but fathomless Atlantic; never before penetrated … save when some foundering vessel has plunged with her hapless company to the eternal silence and darkness of the abyss? Does it seem … but a miracle … that the thoughts of living men … should burn over the cold, green bones of men and women, whose hearts, once as warm as ours, burst as the eternal gulfs closed and roared over them centuries ago?

Does there truly exist an insuperable contradiction between religion and science? Can religion be superseded by science? The answers to these questions have, for centuries, given rise to considerable dispute and, indeed, bitter fighting. Yet, in my own mind there can be no doubt that in both cases a dispassionate consideration can only lead to a negative answer. What complicates the solution, however, is the fact that while most people readily agree on what is meant by ‘science,’ they are likely to differ on the meaning of ‘religion.’

During the century after Newton, it was still possible for a man of unusual attainments to master all fields of scientific knowledge. But by 1800, this had become entirely impracticable.

During the first half of the present century we had an Alexander von Humboldt, who was able to scan the scientific knowledge of his time in its details, and to bring it within one vast generalization. At the present juncture, it is obviously very doubtful whether this task could be accomplished in a similar way, even by a mind with gifts so peculiarly suited for the purpose as Humboldt's was, and if all his time and work were devoted to the purpose.

During the half-century that has elapsed since the enunciation of the cell-theory by Schleiden and Schwann, in 1838-39, it has became ever more clearly apparent that the key to all ultimate biological problems must, in the last analysis, be sought in the cell. It was the cell-theory that first brought the structure of plants and animals under one point of view by revealing their common plan of organization. It was through the cell-theory that Kolliker and Remak opened the way to an understanding of the nature of embryological development, and the law of genetic continuity lying at the basis of inheritance. It was the cell-­theory again which, in the hands of Virchaw and Max Schultze, inaugurated a new era in the history of physiology and pathology, by showing that all the various functions of the body, in health and in disease, are but the outward expression of cell­-activities. And at a still later day it was through the cell-theory that Hertwig, Fol, Van Beneden, and Strasburger solved the long-standing riddle of the fertilization of the egg, and the mechanism of hereditary transmission. No other biological generalization, save only the theory of organic evolution, has brought so many apparently diverse phenomena under a common point of view or has accomplished more far the unification of knowledge. The cell-theory must therefore be placed beside the evolution-theory as one of the foundation stones of modern biology.

During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true

Dust consisting of fine fibers of asbestos, which are insoluble and virtually indestructible, may become a public health problem in the near future. At a recent international conference on the biological effects of asbestos sponsored by the New York Academy of Sciences, participants pointed out on the one hand that workers exposed to asbestos dust are prone in later life to develop lung cancer, and on the other hand that the use of this family of fibrous silicate compounds has expanded enormously during the past few decades. A laboratory curiosity 100 years ago, asbestos today is a major component of building materials.

Earlier this week … scientists announced the completion of a task that once seemed unimaginable; and that is, the deciphering of the entire DNA sequence of the human genetic code. This amazing accomplishment is likely to affect the 21st century as profoundly as the invention of the computer or the splitting of the atom affected the 20th century. I believe that the 21st century will be the century of life sciences, and nothing makes that point more clearly than this momentous discovery. It will revolutionize medicine as we know it today.

Electricity is but yet a new agent for the arts and manufactures, and, doubtless, generations unborn will regard with interest this century, in which it has been first applied to the wants of mankind.

England was nothing, compared to continental nations until she had become commercial … until about the middle of the last century, when a number of ingenious and inventive men, without apparent relation to each other, arose in various parts of the kingdom, succeeded in giving an immense impulse to all the branches of the national industry; the result of which has been a harvest of wealth and prosperity, perhaps without a parallel in the history of the world.

Eventually the process of aging, which is unlikely to be simple, should be understandable. Hopefully some of its processes can be slowed down or avoided. In fact, in the next century, we shall have to tackle the question of the preferred form of death.

Every 12 years Jupiter returns to the same position in the sky; every 370 days it disappears in the fire of the Sun in the evening to the west, 30 days later it reappears in the morning to the east...[Observation in 4th century B.C.]

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.

Everyone working in science, no matter their politics, has a stake in cleaning up the mess revealed by the East Anglia emails. Science is on the credibility bubble. If it pops, centuries of what we understand to be the role of science go with it.

Everything is becoming science fiction; From the margins of an almost invisible literature has sprung the intact reality of the 20th century

Five centuries ago the printing press sparked a radical reshaping of the nature of education. By bringing a master’s words to those who could not hear a master’s voice, the technology of printing dissolved the notion that education must be reserved for those with the means to hire personal tutors. Today we are approaching a new technological revolution, one whose impact on education may be as far-reaching as that of the printing press: the emergence of powerful computers that are sufficiently inexpensive to be used by students for learning, play and exploration. It is our hope that these powerful but simple tools for creating and exploring richly interactive environments will dissolve the barriers to the production of knowledge as the printing press dissolved the barriers to its transmission.

For centuries and millenniums, God rested while man invented wheelbarrows and cars. God had not thought of inventing dynamite. Did he realize his own shortcomings when he saw what we could do? Did he approve of our remodeling of everything he had done?

For centuries the concept that food bore a relationship to anemia had been vaguely expressed in the literature. It had been shown that liver and kidneys, rich in complete proteins, promoted the growth of animals, and that substances in liver could enhance cell division. It was likewise recognized that liver-feeding could benefit patients with sprue…and pellagra. These were among the reasons that led to the choice of liver as a substance likely to enhance blood formation.

For forty-nine months between 1968 and 1972, two dozen Americans had the great good fortune to briefly visit the Moon. Half of us became the first emissaries from Earth to tread its dusty surface. We who did so were privileged to represent the hopes and dreams of all humanity. For mankind it was a giant leap for a species that evolved from the Stone Age to create sophisticated rockets and spacecraft that made a Moon landing possible. For one crowning moment, we were creatures of the cosmic ocean, an epoch that a thousand years hence may be seen as the signature of our century.

For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.

For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.

For many centuries chemists labored to change lead into precious gold, and eventually found that precious uranium turned to lead without any human effort at all.

For more than half a century, Martin Gardner has been the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.

For most of history, man has had to fight nature to survive; in this century he is beginning to realize that, in order to survive, he must protect it.

Fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have [played] … an historical role … in the development of pure mathematics. A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th. Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton. Modern mathematics began with Cantor’s set theory and Peano’s space-filling curve. Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. These new structures were regarded … as “pathological,” .… as a “gallery of monsters,” akin to the cubist paintings and atonal music that were upsetting established standards of taste in the arts at about the same time. The mathematicians who created the monsters regarded them as important in showing that the world of pure mathematics contains a richness of possibilities going far beyond the simple structures that they saw in Nature. Twentieth-century mathematics flowered in the belief that it had transcended completely the limitations imposed by its natural origins.
Now, as Mandelbrot points out, … Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.

From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.

Genetics as a whole is the great over-hyped science, and geneticists know that even if they don't say it. All that genetics really is is anatomy plus an enormous research group grant. It's what anatomists did in the fifteenth century-looking at the heart and seeing how it worked. Now, we are doing the same with DNA

Giordano Bruno was the martyr; though the cause for which he suffered was not that of science, but that of free imaginative speculation. His death in the year 1600 ushered in the first century of modern science in the strict sense of the term.

Half a century ago Oswald (1910) distinguished classicists and romanticists among the scientific investigators: the former being inclined to design schemes and to use consistently the deductions from working hypotheses; the latter being more fit for intuitive discoveries of functional relations between phenomena and therefore more able to open up new fields of study. Examples of both character types are Werner and Hutton. Werner was a real classicist. At the end of the eighteenth century he postulated the theory of “neptunism,” according to which all rocks including granites, were deposited in primeval seas. It was an artificial scheme, but, as a classification system, it worked quite satisfactorily at the time. Hutton, his contemporary and opponent, was more a romanticist. His concept of “plutonism” supposed continually recurrent circuits of matter, which like gigantic paddle wheels raise material from various depths of the earth and carry it off again. This is a very flexible system which opens the mind to accept the possible occurrence in the course of time of a great variety of interrelated plutonic and tectonic processes.

He [Winston Churchill] is rather like a layer cake. One layer was certainly seventeenth century. The eighteenth century in him is obvious. There was the nineteenth century, and a large slice, of course, of the twentieth century; and another, curious, layer which may possibly have been the twenty-first.

He was not a mathematician–he never even took a maths class after high school–yet Martin Gardner, who has died aged 95, was arguably the most influential and inspirational figure in mathematics in the second half of the last century.

Historically [chemistry] arose from a constellation of interests: the empirically based technologies of early metallurgists, brewers, dyers, tanners, calciners and pharmacists; the speculative Greek philosphers' concern whether brute matter was invariant or transformable; the alchemists' real or symbolic attempts to achieve the transmutation of base metals into gold; and the iatrochemists' interst in the chemistry and pathology of animal and human functions. Partly because of the sheer complexity of chemical phenomena, the absence of criteria and standards of purity, and uncertainty over the definition of elements ... but above all because of the lack of a concept of the gaseous state of matter, chemistry remained a rambling, puzzling and chaotic area of natural philosophy until the middle of the eighteenth century.

How strange it would be if the final theory were to be discovered in our lifetimes! The discovery of the final laws of nature will mark a discontinuity in human intellectual history, the sharpest that has occurred since the beginning of modern science in the seventeenth century. Can we now imagine what that would be like?

However, the small probability of a similar encounter [of the earth with a comet], can become very great in adding up over a huge sequence of centuries. It is easy to picture to oneself the effects of this impact upon the Earth. The axis and the motion of rotation changed; the seas abandoning their old position to throw themselves toward the new equator; a large part of men and animals drowned in this universal deluge, or destroyed by the violent tremor imparted to the terrestrial globe.

Human interest in exploring the heavens goes back centuries. This is what human nature is all about.

Hyper-selectionism has been with us for a long time in various guises; for it represents the late nineteenth century’s scientific version of the myth of natural harmony–all is for the best in the best of all possible worlds (all structures well designed for a definite purpose in this case). It is, indeed, the vision of foolish Dr. Pangloss, so vividly satirized by Voltaire in Candide–the world is not necessarily good, but it is the best we could possibly have.

I attained a triumph so complete that it is now rare to meet an American with marks of small pox on his face... Benefits are valuable according to their duration and extent, like the showers from heaven, but the benign remedy Vaccination saves millions of lives every century, like the blessing of the sun, universal and everlasting.
(Remark made near the end of his life.)

I believe as a matter of faith that the extension of space travel to the limits of the solar system will probably be accomplished in several decades, perhaps before the end of the century. Pluto is 4000 million miles from the sun. The required minimum launching velocity is about 10 miles per second and the transit time is 46 years. Thus we would have to make the velocity considerably higher to make the trip interesting to man. Travel to the stars is dependent on radically new discoveries in science and technology. The nearest star is 25 million million miles way and requires a travel time of more than four years at the speed of light. Prof. Dr. Ing. E. Sanger has speculated that velocities comparable with the speed of light might be attained in the next century, but such extrapolation of current technology is probably not very reliable.

I hate it. I just do. That [artificial turf], local news, the IRS, and hair dryers are the four worst inventions of the century.

I have said that mathematics is the oldest of the sciences; a glance at its more recent history will show that it has the energy of perpetual youth. The output of contributions to the advance of the science during the last century and more has been so enormous that it is difficult to say whether pride in the greatness of achievement in this subject, or despair at his inability to cope with the multiplicity of its detailed developments, should be the dominant feeling of the mathematician. Few people outside of the small circle of mathematical specialists have any idea of the vast growth of mathematical literature. The Royal Society Catalogue contains a list of nearly thirty- nine thousand papers on subjects of Pure Mathematics alone, which have appeared in seven hundred serials during the nineteenth century. This represents only a portion of the total output, the very large number of treatises, dissertations, and monographs published during the century being omitted.

I saw [Linus Pauling] as a brilliant lecturer and a man with a fantastic memory, and a great, great showman. I think he was the century’s greatest chemist. No doubt about it.

I suspect that the changes that have taken place during the last century in the average man's fundamental beliefs, in his philosophy, in his concept of religion. in his whole world outlook, are greater than the changes that occurred during the preceding four thousand years all put together. ... because of science and its applications to human life, for these have bloomed in my time as no one in history had had ever dreamed could be possible.

I think that the discovery of antimatter was perhaps the biggest jump of all the big jumps in physics in our century.

I think the next [21st] century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don’t know how the laws fit together, and what happens under extreme conditions. But I expect we will find a complete unified theory sometime this century. The is no limit to the complexity that we can build using those basic laws.
[Answer to question: Some say that while the twentieth century was the century of physics, we are now entering the century of biology. What do you think of this?]

If Einstein’s theory [of relativity] should prove to be correct, as I expect it will, he will be considered the Copernicus of the twentieth century.

If history is any guide at all, it seems to me to suggest that there is a final theory. In this century we have seen a convergence of the arrows of explanation, like the convergence of meridians toward the North Pole.

If the great story of the last century was the conflict among various political ideologies—communism, fascism and democracy—then the great narrative of this century will be the changes wrought by astonishing scientific breakthroughs

If today you can take a thing like evolution and make it a crime to teach it in the public schools, tomorrow you can make it a crime to teach it in the private schools, and next year you can make it a crime to teach it to the hustings or in the church. At the next session you may ban books and the newspapers. Soon you may set Catholic against Protestant and Protestant against Protestant, and try to foist your own religion upon the minds of men. If you can do one you can do the other. Ignorance and fanaticism are ever busy and need feeding. Always it is feeding and gloating for more. Today it is the public school teachers; tomorrow the private. The next day the preachers and the lecturers, the magazines, the books, the newspapers. After a while, Your Honor, it is the setting of man against man and creed against creed until with flying banners and beating drums we are marching backward to the glorious ages of the sixteenth century when bigots lighted fagots to burn the men who dared to bring any intelligence and enlightenment and culture to the human mind.

If we have learned anything at all in this century, it is that all new technologies will be put to use, sooner or later, for better or worse, as it is in our nature to do

In 1768, some peasants, near Luce in France, heard a thunderclap and saw a large stone fall from the sky. Reports of this strange phenomenon reached the French Academy of Sciences. The Academy asked Lavoisier, the premier chemist, to investigate. Lavoisier knew that stones do not fall out of the sky; so, in his knowledgeable arrogance, he reported that the witnesses were either lying or mistaken. The academy did not accept the fact of meteorites until the following century.

In a library we are surrounded by many hundreds of dear friends, but they are imprisoned by an enchanter in these paper and leathern boxes; and though they know us, and have been waiting two, ten, or twenty centuries for us,—some of them,—and are eager to give us a sign and unbosom themselves, it is the law of their limbo that they must not speak until spoken to; and as the enchanter has dressed them, like battalions of infantry, in coat and jacket of one cut, by the thousand and ten thousand, your chance of hitting on the right one is to be computed by the arithmetical rule of Permutation and Combination,—not a choice out of three caskets, but out of half a million caskets, all alike.

In Cairo, I secured a few grains of wheat that had slumbered for more than thirty centuries in an Egyptian tomb. As I looked at them this thought came into my mind: If one of those grains had been planted on the banks of the Nile the year after it grew, and all its lineal descendants had been planted and replanted from that time until now, its progeny would to-day be sufficiently numerous to feed the teeming millions of the world. An unbroken chain of life connects the earliest grains of wheat with the grains that we sow and reap. There is in the grain of wheat an invisible something which has power to discard the body that we see, and from earth and air fashion a new body so much like the old one that we cannot tell the one from the other.…This invisible germ of life can thus pass through three thousand resurrections.

In fact, it is often stated that of all the theories proposed in this century, the silliest is quantum theory. Some say that the only thing that quantum theory has going for it, in fact, is that it is unquestionably correct.

In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century (Hermite, 1822-1901) could say without exaggeration, “Abel has left mathematicians enough to keep them busy for five hundred years.” Asked how he had done all this in the six or seven years of his working life, Abel replied, “By studying the masters, not the pupils.”

In India, rice is grown below sea level in Kuttanad in Kerala and at above 3,000 meters in Kashmir and Himachal Pradesh. The importance of rice as the mainstay of a sustainable food security system will grow during this century because of climate change. No other cereal has the resilience of rice to grow under a wide range of growing conditions.

In my considered opinion the peer review system, in which proposals rather than proposers are reviewed, is the greatest disaster visited upon the scientific community in this century. No group of peers would have approved my building the 72-inch bubble chamber. Even Ernest Lawrence told me he thought I was making a big mistake. He supported me because he knew my track record was good. I believe that U.S. science could recover from the stultifying effects of decades of misguided peer reviewing if we returned to the tried-and-true method of evaluating experimenters rather than experimental proposals. Many people will say that my ideas are elitist, and I certainly agree. The alternative is the egalitarianism that we now practice and I’ve seen nearly kill basic science in the USSR and in the People's Republic of China.

In our century the conceptions substitution and substitution group, transformation and transformation group, operation and operation group, invariant, differential invariant and differential parameter, appear more and more clearly as the most important conceptions of mathematics.

In the course of the last century science has become so dizzy with its successes, that it has forgotten to ask the pertinent questions—or refused to ask them under the pretext that they are meaningless, and in any case not the scientists concern.

In the field of thinking, the whole history of science from geocentrism to the Copernican revolution, from the false absolutes of Aristotle’s physics to the relativity of Galileo’s principle of inertia and to Einstein’s theory of relativity, shows that it has taken centuries to liberate us from the systematic errors, from the illusions caused by the immediate point of view as opposed to “decentered” systematic thinking.

In the great debates of early-nineteenth century geology, catastrophists followed the stereotypical method of objective science-empirical literalism. They believed what they saw, interpolated nothing, and read the record of the rocks directly.

In the history of physics, there have been three great revolutions in thought that first seemed absurd yet proved to be true. The first proposed that the earth, instead of being stationary, was moving around at a great and variable speed in a universe that is much bigger than it appears to our immediate perception. That proposal, I believe, was first made by Aristarchos two millenia ago ... Remarkably enough, the name Aristarchos in Greek means best beginning.
[The next two revolutions occurred ... in the early part of the twentieth century: the theory of relativity and the science of quantum mechanics...]

In the main, Bacon prophesied the direction of subsequent progress. But he “anticipated” the advance. He did not see that the new science was for a long time to be worked in the interest of old ends of human exploitation. He thought that it would rapidly give man new ends. Instead, it put at the disposal of a class the means to secure their old ends of aggrandizement at the expense of another class. The industrial revolution followed, as he foresaw, upon a revolution in scientific method. But it is taking the revolution many centuries to produce a new mind.

In the next twenty centuries … humanity may begin to understand its most baffling mystery—where are we going? The earth is, in fact, traveling many thousands of miles per hour in the direction of the constellation Hercules—to some unknown destination in the cosmos. Man must understand his universe in order to understand his destiny. Mystery, however, is a very necessary ingredient in our lives. Mystery creates wonder and wonder is the basis for man’s desire to understand. Who knows what mysteries will be solved in our lifetime, and what new riddles will become the challenge of the new generation? Science has not mastered prophesy. We predict too much for the next year yet far too little for the next ten. Responding to challenges is one of democracy’s great strengths. Our successes in space can be used in the next decade in the solution of many of our planet’s problems.

In the nineteenth century men lost their fear of God and acquired a fear of microbes.

In the past century, there were more changes than in the previous thousand years. The new century will see changes that will dwarf those of the last.
Referring to the 19th and 20th centuries.

In the past, you wouldn’t have had any problem in getting a countryman to explain the difference between a blackbird and a song thrush, but you might have that difficulty with a kid now. Equally, if you asked a chap about gorillas in the 19th-century, he wouldn’t have heard of the creatures, but today an urban boy knows all about them.

In this century the professional philosophers have let the physicists get away with murder. It is a safe bet that no other group of scientists could have passed off and gained acceptance for such an extraordinary principle as complementarity, nor succeeded in elevating indeterminacy to a universal law.

Indeed, we need not look back half a century to times which many now living remember well, and see the wonderful advances in the sciences and arts which have been made within that period. Some of these have rendered the elements themselves subservient to the purposes of man, have harnessed them to the yoke of his labors and effected the great blessings of moderating his own, of accomplishing what was beyond his feeble force, and extending the comforts of life to a much enlarged circle, to those who had before known its necessaries only.

Indians walk softly and hurt the landscape hardly more than the birds and squirrels, and their brush and bark huts last hardly longer than those of wood rats, while their more enduring monuments, excepting those wrought on the forests by the fires they made to improve their hunting grounds, vanish in a few centuries.

IODINE
It was Courtois discover'd Iodine
(In the commencement of this century),
Which, with its sisters, bromine and chlorine,
Enjoys a common parentage - the sea;
Although sometimes 'tis found, with other things,
In minerals and many saline springs.

But yet the quantity is so minute
In the great ocean, that a chemist might,
With sensibilities the most acute,
Have never brought this element to light,
Had he not thought it were as well to try
Where ocean's treasures concentrated lie.

And Courtois found that several plants marine,
Sponges, et cetera, exercise the art
Of drawing from the sea its iodine
In quantities sufficient to impart
Its properties; and he devised a plan
Of bringing it before us - clever man!

It cannot, of course, be stated with absolute certainty that no elements can combine with argon; but it appears at least improbable that any compounds will be formed.

It is a good principle in science not to believe any “fact”—however well attested—until it fits into some accepted frame of reference. Occasionally, of course, an observation can shatter the frame and force the construction of a new one, but that is extremely rare. Galileos and Einsteins seldom appear more than once per century, which is just as well for the equanimity of mankind.