…we all had to learn a number of XIXth century rules—such as Markownikov’s rule for addition to olefins, Thiele’s 1:4—addition rules for conjugated systems and Crum Brown’s rule for aromatic substitution. It was just like learning Latin grammar.

[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.

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.

As the nineteenth century drew to a close, scientists could reflect with satisfaction that they had pinned down most of the mysteries of the physical world: electricity, magnetism, gases, optics, acoustics, kinetics and statistical mechanics … all had fallen into order before them. They had discovered the X ray, the cathode ray, the electron, and radioactivity, invented the ohm, the watt, the Kelvin, the joule, the amp, and the little erg.

At the beginning of its existence as a science, biology was forced to take cognizance of the seemingly boundless variety of living things, for no exact study of life phenomena was possible until the apparent chaos of the distinct kinds of organisms had been reduced to a rational system. Systematics and morphology, two predominantly descriptive and observational disciplines, took precedence among biological sciences during the eighteenth and nineteenth centuries. More recently physiology has come to the foreground, accompanied by the introduction of quantitative methods and by a shift from the observationalism of the past to a predominance of experimentation.

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.

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.

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.

In a training period I continue to believe that the best start is with the experimentally prepared situation. Principally because it is in this that it is easiest to illustrate controlled variability, but there is no compelling reason why all experiments should be shaped to the conventional forms of the psychophysical methods. In any case the psychologist must refuse to be limited by those formalised statements of scientific experiment, which grew up with the logical methodologists of the mid-19th century. There are no psychological experiments in which the conditions are all under control; in which one condition can be varied independently of the rest, or even in which the concomitant variation of two specified conditions alone can be arranged and considered.

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.

It [the nineteenth century] was the time of those classical explorers who set out into the unknown [of Africa], without the expense of a large expedition, alone or with only a few companions, for whom traveling was an end in itself, unselfish and harmless, with little money and with no blood sacrifice other than their own.

It is a temptation for philosophers that they should weave a fairy tale of the adjustment of factors; and then as an appendix introduce the notion of frustration, as a secondary aspect. I suggest to you that this is the criticism to be made on the monistic idealisms of the nineteenth century, and even of the great Spinoza. It is quite incredible that the Absolute, as conceived in monistic philosophy, should evolve confusion about its own details.

Kepler’s discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler—such penetrating minds as Descartes and Pascal—were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.

No medieval schoolman has been singled out as a precursor more often than the French scholastic Nicole Oresme.This brilliant scholar has been credited with … the framing of Gresham’s law before Gresham, the invention of analytic geometry before Descartes, with propounding structural theories of compounds before nineteenth century organic chemists, with discovering the law of free fall before Galileo, and with advocating the rotation of the Earth before Copernicus. None of these claims is, in fact, true, although each is based on discussion by Oresme of some penetration and originality …

Now, it may be stretching an analogy to compare epidemics of cholera—caused by a known agent—with that epidemic of violent crime which is destroying our cities. It is unlikely that our social problems can be traced to a single, clearly defined cause in the sense that a bacterial disease is ‘caused’ by a microbe. But, I daresay, social science is about as advanced in the late twentieth century as bacteriological science was in the mid nineteenth century. Our forerunners knew something about cholera; they sensed that its spread was associated with misdirected sewage, filth, and the influx of alien poor into crowded, urban tenements. And we know something about street crime; nowhere has it been reported that a member of the New York Stock Exchange has robbed ... at the point of a gun. Indeed, I am naively confident that an enlightened social scientist of the next century will be able to point out that we had available to us at least some of the clues to the cause of urban crime.

One of the most conspicuous and distinctive features of mathematical thought in the nineteenth century is its critical spirit. Beginning with the calculus, it soon permeates all analysis, and toward the close of the century it overhauls and recasts the foundations of geometry and aspires to further conquests in mechanics and in the immense domains of mathematical physics. … A searching examination of the foundations of arithmetic and the calculus has brought to light the insufficiency of much of the reasoning formerly considered as conclusive.

Our understanding of the causes of biological diversity is still crude. The science addressing it can be generously put at about the level of physics in the late nineteenth century.

Peer reviewers go for orthodoxy ... Many of the great 19th-century discoveries were made by men who had independent wealth—Charles Darwin is the prototype. They trusted themselves.
[Commenting that the anonymous peer review process is the enemy of scientific creativity]

Scientists wrote beautifully through the 19th century and on into the early 20th. But somewhere after that, coincident with the explosive growth of research, the art of writing science suffered a grave setback, and the stultifying convention descended that the best scientific prose should sound like a non-human author addressing a mechanical reader.

Since the beginning of the century, computational procedures have become so complicated that any progress by those means has become impossible, without the elegance which modern mathematicians have brought to bear on their research, and by means of which the spirit comprehends quickly and in one step a great many computations.
It is clear that elegance, so vaunted and so aptly named, can have no other purpose. …
[But, the simplifications produced by this elegance will soon outrun the problems supplied by analysis. What happens then?]
Go to the roots, of these calculations! Group the operations. Classify them according to their complexities rather than their appearances! This, I believe, is the mission of future mathematicians. This is the road on which I am embarking in this work.

Sometimes I wonder whether there is any such thing as biology. The word was invented rather late—in 1809—and other words like botany, zoology, physiology, anatomy, have much longer histories and in general cover more coherent and unified subject matters. … I would like to see the words removed from dictionaries and college catalogues. I think they do more harm than good because they separate things that should not be separated…

The end of the eighteenth and the beginning of the nineteenth century were remarkable for the small amount of scientific movement going on in this country, especially in its more exact departments. ... Mathematics were at the last gasp, and Astronomy nearly so—I mean in those members of its frame which depend upon precise measurement and systematic calculation. The chilling torpor of routine had begun to spread itself over all those branches of Science which wanted the excitement of experimental research.

The essential unity of ecclesiastical and secular institutions was lost during the 19th century, to the point of senseless hostility. Yet there was never any doubt as to the striving for culture. No one doubted the sacredness of the goal. It was the approach that was disputed.

The golden age of mathematics—that was not the age of Euclid, it is ours. Ours is the age when no less than six international congresses have been held in the course of nine years. It is in our day that more than a dozen mathematical societies contain a growing membership of more than two thousand men representing the centers of scientific light throughout the great culture nations of the world. It is in our time that over five hundred scientific journals are each devoted in part, while more than two score others are devoted exclusively, to the publication of mathematics. It is in our time that the Jahrbuch über die Fortschritte der Mathematik, though admitting only condensed abstracts with titles, and not reporting on all the journals, has, nevertheless, grown to nearly forty huge volumes in as many years. It is in our time that as many as two thousand books and memoirs drop from the mathematical press of the world in a single year, the estimated number mounting up to fifty thousand in the last generation. Finally, to adduce yet another evidence of a similar kind, it requires not less than seven ponderous tomes of the forthcoming Encyclopaedie der Mathematischen Wissenschaften to contain, not expositions, not demonstrations, but merely compact reports and bibliographic notices sketching developments that have taken place since the beginning of the nineteenth century.

The great error of the 19th century, in morality as well as in science and art, has been to mingle and confound man and nature without pausing to consider that in art as in science and morality he is a man only in so far as he distinguishes himself from nature and makes himself an exception to it.

The greatest invention of the nineteenth century was the invention of the method of invention.

The most revolutionary invention of the XIX century was the artificial sterilization of marriage.

The nineteenth century is a turning point in history, simply on account of the work of two men, Darwin and Renan, the one the critic of the Book of Nature, the other the critic of the books of God. Not to recognise this is to miss the meaning of one of the most important eras in the progress of the world.

The nineteenth century which prides itself upon the invention of steam and evolution, might have derived a more legitimate title to fame from the discovery of pure mathematics.

The nineteenth century will ever be known as the one in which the influences of science were first fully realised in civilised communities; the scientific progress was so gigantic that it seems rash to predict that any of its successors can be more important in the life of any nation.

The nineteenth century, which prided itself upon the invention of steam and evolution, might have derived a more legitimate title to fame from the discovery of pure mathematics.

The private motives of scientists are not the trend of science. The trend of science is made by the needs of society: navigation before the eighteenth century, manufacture thereafter; and in our age I believe the liberation of personality. Whatever the part which scientists like to act, or for that matter which painters like to dress, science shares the aims of our society just as art does.

The second law of thermodynamics is, without a doubt, one of the most perfect laws in physics. Any reproducible violation of it, however small, would bring the discoverer great riches as well as a trip to Stockholm. The world’s energy problems would be solved at one stroke… . Not even Maxwell’s laws of electricity or Newton’s law of gravitation are so sacrosanct, for each has measurable corrections coming from quantum effects or general relativity. The law has caught the attention of poets and philosophers and has been called the greatest scientific achievement of the nineteenth century.

There is no inductive method which could lead to the fundamental concepts of physics. Failure to understand this fact constituted the basic philosophical error of so many investigators of the nineteenth century.

These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. “Mathematics in general is fundamentally the science of self-evident things.” ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense—that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not.

We need science education to produce scientists, but we need it equally to create literacy in the public. Man has a fundamental urge to comprehend the world about him, and science gives today the only world picture which we can consider as valid. It gives an understanding of the inside of the atom and of the whole universe, or the peculiar properties of the chemical substances and of the manner in which genes duplicate in biology. An educated layman can, of course, not contribute to science, but can enjoy and participate in many scientific discoveries which as constantly made. Such participation was quite common in the 19th century, but has unhappily declined. Literacy in science will enrich a person’s life.

We praise the eighteenth century for concerning itself chiefly with analysis. The task remaining to the nineteenth is to discover the false syntheses which prevail, and to analyse their contents anew.

What is peculiar and new to the [19th] century, differentiating it from all its predecessors, is its technology. It was not merely the introduction of some great isolated inventions. It is impossible not to feel that something more than that was involved. … The process of change was slow, unconscious, and unexpected. In the nineteeth century, the process became quick, conscious, and expected. … The whole change has arisen from the new scientific information. Science, conceived not so much in its principles as in its results, is an obvious storehouse of ideas for utilisation. … Also, it is a great mistake to think that the bare scientific idea is the required invention, so that it has only to be picked up and used. An intense period of imaginative design lies between. One element in the new method is just the discovery of how to set about bridging the gap between the scientific ideas, and the ultimate product. It is a process of disciplined attack upon one difficulty after another This discipline of knowledge applies beyond technology to pure science, and beyond science to general scholarship. It represents the change from amateurs to professionals. … But the full self-conscious realisation of the power of professionalism in knowledge in all its departments, and of the way to produce the professionals, and of the importance of knowledge to the advance of technology, and of the methods by which abstract knowledge can be connected with technology, and of the boundless possibilities of technological advance,—the realisation of all these things was first completely attained in the nineteeth century.

When we look back beyond one hundred years over the long trails of history, we see immediately why the age we live in differs from all other ages in human annals. … It remained stationary in India and in China for thousands of years. But now it is moving very fast. … A priest from Thebes would probably have felt more at home at the council of Trent, two thousand years after Thebes had vanished, than Sir Isaac Newton at a modern undergraduate physical society, or George Stephenson in the Institute of Electrical Engineers. The changes have have been so sudden and so gigantic, that no period in history can be compared with the last century. The past no longer enables us even dimly to measure the future.

With a single exception, it may be affirmed that units of volume now [1893] in use were originally in no way related to units of length, most of them being of accidental and now unknown origin. That a legal bushel in the United States must contain 2150.42 cubic inches is convincing evidence that the foot or the yard has no place in its ancestry.