As we continue to improve our understanding of the basic science on which applications increasingly depend, material benefits of this and other kinds are secured for the future.

If experiments are performed thousands of times at all seasons and in every place without once producing the effects mentioned by your philosophers, poets, and historians, this will mean nothing and we must believe their words rather our own eyes? But what if I find for you a state of the air that has all the conditions you say are required, and still the egg is not cooked nor the lead ball destroyed? Alas! I should be wasting my efforts... for all too prudently you have secured your position by saying that 'there is needed for this effect violent motion, a great quantity of exhalations, a highly attenuated material and whatever else conduces to it.' This 'whatever else' is what beats me, and gives you a blessed harbor, a sanctuary completely secure.

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 one department of his [Joseph Black’s] lecture he exceeded any I have ever known, the neatness and unvarying success with which all the manipulations of his experiments were performed. His correct eye and steady hand contributed to the one; his admirable precautions, foreseeing and providing for every emergency, secured the other. I have seen him pour boiling water or boiling acid from a vessel that had no spout into a tube, holding it at such a distance as made the stream’s diameter small, and so vertical that not a drop was spilt. While he poured he would mention this adaptation of the height to the diameter as a necessary condition of success. I have seen him mix two substances in a receiver into which a gas, as chlorine, had been introduced, the effect of the combustion being perhaps to produce a compound inflammable in its nascent state, and the mixture being effected by drawing some string or wire working through the receiver's sides in an air-tight socket. The long table on which the different processes had been carried on was as clean at the end of the lecture as it had been before the apparatus was planted upon it. Not a drop of liquid, not a grain of dust remained.

It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws.

Next came the patent laws. These began in England in 1624, and in this country with the adoption of our Constitution. Before then any man [might] instantly use what another man had invented, so that the inventor had no special advantage from his own invention. The patent system changed this, secured to the inventor for a limited time exclusive use of his inventions, and thereby added the fuel of interest to the fire of genius in the discovery and production of new and useful things.

No! What we need are not prohibitory marriage laws, but a reformed society, an educated public opinion which will teach individual duty in these matters. And it is to the women of the future that I look for the needed reformation. Educate and train women so that they are rendered independent of marriage as a means of gaining a home and a living, and you will bring about natural selection in marriage, which will operate most beneficially upon humanity. When all women are placed in a position that they are independent of marriage, I am inclined to think that large numbers will elect to remain unmarried—in some cases, for life, in others, until they encounter the man of their ideal. I want to see women the selective agents in marriage; as things are, they have practically little choice. The only basis for marriage should be a disinterested love. I believe that the unfit will be gradually eliminated from the race, and human progress secured, by giving to the pure instincts of women the selective power in marriage. You can never have that so long as women are driven to marry for a livelihood.

One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.

Only a few years ago, it was generally supposed that by crossing two somewhat different species or varieties a mongrel might be produced which might, or more likely might not, surpass its parents. The fact that crossing was only the first step and that selection from the numerous variations secured in the second and a few succeeding generations was the real work of new plant creation had never been appreciated; and to-day its significance is not fully understood either by breeders or even by many scientific investigators along these very lines.

Science deals with judgments on which it is possible to obtain universal agreement. These judgments do not concern individual facts and events, but the invariable association of facts and events known as the laws of science. Agreement is secured by observation and experiment—impartial courts of appeal to which all men must submit if they wish to survive. The laws are grouped and explained by theories of ever increasing generality. The theories at first are ex post facto—merely plausible interpretations of existing bodies of data. However, they frequently lead to predictions that can be tested by experiments and observations in new fields, and, if the interpretations are verified, the theories are accepted as working hypotheses until they prove untenable. The essential requirements are agreement on the subject matter and the verification of predictions. These features insure a body of positive knowledge that can be transmitted from person to person, and that accumulates from generation to generation.

The expenditure [on building railways] of £286,000,000 by the people has secured to us the advantages of internal communication all but perfect,—of progress in science and arts unexampled at any period of the history of the world,—of national progress almost unchecked, and of prosperity and happiness increased beyond all precedent.

The great horde of physicians are always servile imitators, who can neither perceive nor correct the faults of their system, and are always ready to growl at and even to worry the ingenious person that could attempt it. Thus was the system of Galen secured in the possession of the schools of physic.

There are about 3,000,000 people seriously ill in the United States…. More than half of this illness is preventable. If we count the value of each life lost at only $1700 and reckon the average earning lost by illness at $700 a year for grown men, we find that the economic gain from mitigation of preventable disease in the United States would exceed $1,500,000,000 a year. … This gain … can be secured through medical investigation and practice, school and factory hygiene, restriction of labor by women and children, the education of the people in both public and private hygiene, and through improving the efficiency of our health service, municipal, state, and national.

There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured … Of these sciences the gate and key is mathematics … He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world.

Undeveloped though the science [of chemistry] is, it already has great power to bring benefits. Those accruing to physical welfare are readily recognized, as in providing cures, improving the materials needed for everyday living, moving to ameliorate the harm which mankind by its sheer numbers does to the environment, to say nothing of that which even today attends industrial development. And as we continue to improve our understanding of the basic science on which applications increasingly depend, material benefits of this and other kinds are secured for the future.

We must make practice in thinking, or, in other words, the strengthening of reasoning power, the constant object of all teaching from infancy to adult age, no matter what may be the subject of instruction. … Effective training of the reasoning powers cannot be secured simply by choosing this subject or that for study. The method of study and the aim in studying are the all-important things.

When I began my physical studies [in Munich in 1874] and sought advice from my venerable teacher Philipp von Jolly...he portrayed to me physics as a highly developed, almost fully matured science...Possibly in one or another nook there would perhaps be a dust particle or a small bubble to be examined and classified, but the system as a whole stood there fairly secured, and theoretical physics approached visibly that degree of perfection which, for example, geometry has had already for centuries.

When Ramanujan was sixteen, he happened upon a copy of Carr’s Synopsis of Mathematics. This chance encounter secured immortality for the book, for it was this book that suddenly woke Ramanujan into full mathematical activity and supplied him essentially with his complete mathematical equipment in analysis and number theory. The book also gave Ramanujan his general direction as a dealer in formulas, and it furnished Ramanujan the germs of many of his deepest developments.