…it ought to be remembered that there is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things. Because the innovator has for enemies all those who have done well under the old conditions, and lukewarm defenders in those who may do well under the new.

At every major step physics has required, and frequently stimulated, the introduction of new mathematical tools and concepts. Our present understanding of the laws of physics, with their extreme precision and universality, is only possible in mathematical terms.

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.

Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world could have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility. … Our modern power of easy reckoning with decimal fractions is the most miraculous result of a perfect notation.

But as my conclusions have lately been much misrepresented, and it has been stated that I attribute the modification of species exclusively to natural selection, I may be permitted to remark that in the first edition of this work, and subsequently, I placed in a most conspicuous position—namely, at the close of the Introduction—the following words: “I am convinced that natural selection has been the main but not the exclusive means of modification.” This has been of no avail. Great is the power of steady misrepresentation; but the history of science shows that fortunately this power does not long endure.

Earth’s history, which it is the object of Geology to teach, is the true introduction to human history.

First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.

Geology is rapidly taking its place as an introduction to the higher history of man. If the author has sought to exalt a favorite science, it has been with the desire that man—in whom geological history had its consummation, the prophecies of the successive ages their fulfilment—might better comprehend his own nobility and the true purpose of his existence.

I am now convinced that we have recently become possessed of experimental evidence of the discrete or grained nature of matter, which the atomic hypothesis sought in vain for hundreds and thousands of years. The isolation and counting of gaseous ions, on the one hand, which have crowned with success the long and brilliant researches of J.J. Thomson, and, on the other, agreement of the Brownian movement with the requirements of the kinetic hypothesis, established by many investigators and most conclusively by J. Perrin, justify the most cautious scientist in now speaking of the experimental proof of the atomic nature of matter, The atomic hypothesis is thus raised to the position of a scientifically well-founded theory, and can claim a place in a text-book intended for use as an introduction to the present state of our knowledge of General Chemistry.

I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage.

If to be the Author of new things, be a crime; how will the first Civilizers of Men, and makers of Laws, and Founders of Governments escape? Whatever now delights us in the Works of Nature, that excells the rudeness of the first Creation, is New. Whatever we see in Cities, or Houses, above the first wildness of Fields, and meaness of Cottages, and nakedness of Men, had its time, when this imputation of Novelty, might as well have bin laid to its charge. It is not therefore an offence, to profess the introduction of New things, unless that which is introduc'd prove pernicious in itself; or cannot be brought in, without the extirpation of others, that are better.

In the world’s history certain inventions and discoveries occurred of peculiar value, on account of their great efficiency in facilitating all other inventions and discoveries. Of these were the art of writing and of printing, the discovery of America, and the introduction of patent laws. The date of the first … is unknown; but it certainly was as much as fifteen hundred years before the Christian era; the second—printing—came in 1436, or nearly three thousand years after the first. The others followed more rapidly—the discovery of America in 1492, and the first patent laws in 1624.

Just as the introduction of the irrational numbers … is a convenient myth [which] simplifies the laws of arithmetic … so physical objects are postulated entities which round out and simplify our account of the flux of existence… The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.

Kids from all the local villages [on the slopes of Mount Gorongosa in Mozambique] showed up, and I had to be the expert for everything. … These kids went wild. They were listening to everything that I and others had to say about the creatures they were bringing in and the plants and so on. And I realized that anywhere a bioblitz could be a powerful instrument in introducing kids to science.

Medicine rests upon four pillars—philosophy, astronomy, alchemy, and ethics. The first pillar is the philosophical knowledge of earth and water; the second, astronomy, supplies its full understanding of that which is of fiery and airy nature; the third is an adequate explanation of the properties of all the four elements—that is to say, of the whole cosmos—and an introduction into the art of their transformations; and finally, the fourth shows the physician those virtues which must stay with him up until his death, and it should support and complete the three other pillars.

Much later, when I discussed the problem with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life. But this “blunder,” rejected by Einstein, is still sometimes used by cosmologists even today, and the cosmological constant denoted by the Greek letter Λ rears its ugly head again and again and again.

My father’s collection of fossils was practically unnamed, but the appearance of Phillips’ book [Geology of the Yorkshire Coast], in which most of our specimens were figured, enabled us to remedy this defect. Every evening was devoted by us to accomplishing the work. This was my first introduction to true scientific study. … Phillips’ accurate volume initiated an entirely new order of things. Many a time did I mourn over the publication of this book, and the consequences immediately resulting from it. Instead of indulging in the games and idleness to which most lads are prone, my evenings throughout a long winter were devoted to the detested labour of naming these miserable stones. Such is the short-sightedness of boyhood. Pursuing this uncongenial work gave me in my thirteenth year a thorough practical familiarity with the palaeontological treasures of Eastern Yorkshire. This early acquisition happily moulded the entire course of my future life.

My impression about the Panama Canal is that the great revolution it is going to introduce in the trade of the world is in the trade between the east and the west coast of the United States.

Not one of them [formulae] can be shown to have any existence, so that the formula of one of the simplest of organic bodies is confused by the introduction of unexplained symbols for imaginary differences in the mode of combination of its elements… It would be just as reasonable to describe an oak tree as composed of blocks and chips and shavings to which it may be reduced by the hatchet, as by Dr Kolbe’s formula to describe acetic acid as containing the products which may be obtained from it by destructive influences. A Kolbe botanist would say that half the chips are united with some of the blocks by the force parenthesis; the other half joined to this group in a different way, described by a buckle; shavings stuck on to these in a third manner, comma; and finally, a compound of shavings and blocks united together by a fourth force, juxtaposition, is joined to the main body by a fifth force, full stop.

Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.

Science is a human activity, and the best way to understand it is to understand the individual human beings who practise it. Science is an art form and not a philosophical method. The great advances in science usually result from new tools rather than from new doctrines. ... Every time we introduce a new tool, it always leads to new and unexpected discoveries, because Nature's imagination is richer than ours.

Science is organized knowledge; and before knowledge can be organized, some of it must first be possessed. Every study, therefore, should have a purely experimental introduction; and only after an ample fund of observations has been accumulated, should reasoning begin.

Search the scriptures of human achievement and you cannot find any to equal in beneficence the introduction of Anæsthesia, Sanitation, with ail that it includes, and Asepsis—a short half century’s contribution towards the practical solution of the problems of human suffering, regarded as eternal and insoluble.

The advancement of agriculture, commerce and manufactures, by all proper means, will not, I trust, need recommendation. But I cannot forbear intimating to you the expediency of giving effectual encouragement as well to the introduction of new and useful inventions from abroad, as to the exertions of skill and genius in producing them at home.

The history of the knowledge of the phenomena of life and of the organized world can be divided into two main periods. For a long time anatomy, and particularly the anatomy of the human body, was the α and ω of scientific knowledge. Further progress only became possible with the discovery of the microscope. A long time had yet to pass until through Schwann the cell was established as the final biological unit. It would mean bringing coals to Newcastle were I to describe here the immeasurable progress which biology in all its branches owes to the introduction of this concept of the cell concept. For this concept is the axis around which the whole of the modern science of life revolves.

The introduction of men into the lying in chamber in place of female attendants, has increased the suffering and dangers of childbearing women, and brought multiplied injuries and fatalities upon mothers and children; it violates the sensitive feelings of husbands and wives and causes an untold amount of domestic misery. The unlimited intimacy between a male profession and the female population silently and effectually wears away female delicacy and professional morality, and tends probably more than any other cause in existence, to undermine the foundation of public virtue.

The most consequential change in man's view of the world, of living nature and of himself came with the introduction, over a period of some 100 years beginning only in the 18th century, of the idea of change itself, of change over periods of time: in a word, of evolution.

The number of travellers by gigs, the outside of coaches, and on horseback, have, since the introduction of railways, been prodigiously diminished; and as, in addition, the members of the medical faculty having lent their aid to run down the use of water-proof (apparently having found it decided enemy against their best friends colds and catarrhs), the use of the article [the Macintosh] in the form of cloaks, etc., has of late become comparatively extinct.

The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

This is all very fine, but it won’t do—Anatomy—botany—Nonsense! Sir, I know an old woman in Covent Garden, who understands botany better, and as for anatomy, my butcher can dissect a joint full as well; no, young man, all that is stuff; you must go to the bedside, it is there alone you can learn disease!
Comment to Hans Sloane on Robert Boyle’s letter of introduction describing Sloane as a “ripe scholar, a good botanist, a skilful anatomist”.

Those who would legislate against the teaching of evolution should also legislate against gravity, electricity and the unreasonable velocity of light, and also should introduce a clause to prevent the use of the telescope, the microscope and the spectroscope or any other instrument of precision which may in the future be invented, constructed or used for the discovery of truth.

Thus there is everywhere testimony of the same mind, [there is] no place in creation for the introduction of laws varying from the original design. All is one grand unity.

To most ... of us, Russia was as mysterious and remote as the other side of the moon and not much more productive when it came to really new ideas or inventions. A common joke of the time [mid 1940s] said that the Russians could not surreptitiously introduce nuclear bombs in suitcases into the United States because they had not yet been able to perfect a suitcase.

What has been learned in physics stays learned. People talk about scientific revolutions. The social and political connotations of revolution evoke a picture of a body of doctrine being rejected, to be replaced by another equally vulnerable to refutation. It is not like that at all. The history of physics has seen profound changes indeed in the way that physicists have thought about fundamental questions. But each change was a widening of vision, an accession of insight and understanding. The introduction, one might say the recognition, by man (led by Einstein) of relativity in the first decade of this century and the formulation of quantum mechanics in the third decade are such landmarks. The only intellectual casualty attending the discovery of quantum mechanics was the unmourned demise of the patchwork quantum theory with which certain experimental facts had been stubbornly refusing to agree. As a scientist, or as any thinking person with curiosity about the basic workings of nature, the reaction to quantum mechanics would have to be: “Ah! So that’s the way it really is!” There is no good analogy to the advent of quantum mechanics, but if a political-social analogy is to be made, it is not a revolution but the discovery of the New World.

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 there are too many deer in the forest or too many cats in the barn, nature restores the balance by the introduction of a communicable disease or virus.

With the introduction of agriculture mankind entered upon a long period of meanness, misery, and madness, from which they are only now being freed by the beneficent operation of the machine.