... in going over the history of all the inventions for which history could be obtained it became more and more clear that in addition to training and in addition to extensive knowledge, a natural quality of mind was also necessary.

Question: Explain why pipes burst in cold weather.
Answer: People who have not studied acoustics think that Thor bursts the pipes, but we know that is nothing of the kind for Professor Tyndall has burst the mythologies and has taught us that it is the natural behaviour of water (and bismuth) without which all fish would die and the earth be held in an iron grip. (1881)

A few days ago, a Master of Arts, who is still a young man, and therefore the recipient of a modern education, stated to me that until he had reached the age of twenty he had never been taught anything whatever regarding natural phenomena, or natural law. Twelve years of his life previously had been spent exclusively amongst the ancients. The case, I regret to say, is typical. Now we cannot, without prejudice to humanity, separate the present from the past.

A man would have to be an idiot to write a book of laws for an apple tree telling it to bear apples and not thorns, seeing that the apple-tree will do it naturally and far better than any laws or teaching can prescribe.

Darwin abolished special creations, contributed the Origin of Species and hitched all life together in one unbroken procession of Siamese Twins, the whole evolved by natural and orderly processes from one microscopic parent germ.

Every chemical substance, whether natural or artificial, falls into one of two major categories, according to the spatial characteristic of its form. The distinction is between those substances that have a plane of symmetry and those that do not. The former belong to the mineral, the latter to the living world.

Gluttony is the source of all our infirmities, and the fountain of all our diseases. As a lamp is choked by a superabundance of oil, a fire extinguished by excess of fuel, so is the natural health of the body destroyed by intemperate diet.

Good luck is science not yet classified; just as the supernatural is the natural not yet understood.

Human behaviour reveals uniformities which constitute natural laws. If these uniformities did not exist, then there would be neither social science nor political economy, and even the study of history would largely be useless. In effect, if the future actions of men having nothing in common with their past actions, our knowledge of them, although possibly satisfying our curiosity by way of an interesting story, would be entirely useless to us as a guide in life.

I am of the African race, and in the colour which is natural to them of the deepest dye; and it is under a sense of the most profound gratitude to the Supreme Ruler of the Universe.

If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds. To him who is a discoverer in this field the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others, not as creations of thought but as given realities.

In studying the fate of our forest king, we have thus far considered the action of purely natural causes only; but, unfortunately, man is in the woods, and waste and pure destruction are making rapid headway. If the importance of the forests were even vaguely understood, even from an economic standpoint, their preservation would call forth the most watchful attention of government

In the discovery of lemmas the best aid is a mental aptitude for it. For we may see many who are quick at solutions and yet do not work by method ; thus Cratistus in our time was able to obtain the required result from first principles, and those the fewest possible, but it was his natural gift which helped him to the discovery.

It has hitherto been a serious impediment to the progress of knowledge, that is in investigating the origin or causes of natural productions, recourse has generally been had to the examination, both by experiment and reasoning, of what might be rather than what is. The laws or processes of nature we have every reason to believe invariable. Their results from time to time vary, according to the combinations of influential circumstances; but the process remains the same. Like the poet or the painter, the chemist may, and no doubt often' does, create combinations which nature never produced; and the possibility of such and such processes giving rise to such and such results, is no proof whatever that they were ever in natural operation.

Natural ability without education has more often attained to glory and virtue than education without natural ability.

Natural knowledge has not forgone emotion. It has simply taken for itself new ground of emotion, under impulsion from and in sacrifice to that one of its 'values', Truth.

Of possible quadruple algebras the one that had seemed to him by far the most beautiful and remarkable was practically identical with quaternions, and that he thought it most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature’s God must work in the same channels.

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

Pavlov's data on the two fundamental antagonistic nervous processes—stimulation and inhibition—and his profound generalizations regarding them, in particular, that these processes are parts of a united whole, that they are in a state of constant conflict and constant transition of the one to the other, and his views on the dominant role they play in the formation of the higher nervous activity—all those belong to the most established natural—scientific validation of the Marxist dialectal method. They are in complete accord with the Leninist concepts on the role of the struggle between opposites in the evolution, the motion of matter.

Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.

The ends of scientific classification are best answered, when the objects are formed into groups respecting which a greater number of general propositions can be made, and those propositions more important, than could be made respecting any other groups into which the same things could be distributed. ... A classification thus formed is properly scientific or philosophical, and is commonly called a Natural, in contradistinction to a Technical or Artificial, classification or arrangement.

The laws of Coexistence;—the adaptation of structure to function; and to a certain extent the elucidation of natural affinities may be legitimately founded upon the examination of fully developed species;—But to obtain an insight into the laws of development,—the signification or bedeutung, of the parts of an animal body demands a patient examination of the successive stages of their development, in every group of Animals.

The nature of things betrays itself more readily under the vexations of art than in its natural freedom.

The progress of synthesis, or the building up of natural materials from their constituent elements, proceeds apace. Even some of the simpler albuminoids, a class of substances of great importance in the life process, have recently been artificially prepared. ... Innumerable entirely new compounds have been produced in the last century. The artificial dye-stuffs, prepared from materials occurring in coal-tar, make the natural colours blush. Saccharin, which is hundreds of times sweeter than sugar, is a purely artificial substance. New explosives, drugs, alloys, photographic substances, essences, scents, solvents, and detergents are being poured out in a continuous stream.

The sciences have sworn among themselves an inviolable partnership; it is almost impossible to separate them, for they would rather suffer than be torn apart; and if anyone persists in doing so, he gets for his trouble only imperfect and confused fragments. Yet they do not arrive all together, but they hold each other by the hand so that they follow one another in a natural order which it is dangerous to change, because they refuse to enter in any other way where they are called. ...

To be worth of the name, an experimenter must be at once theorist and practitioner. While he must completely master the art of establishing experimental facts, which are the materials of science, he must also clearly understand the scientific principles which guide his reasoning through the varied experimental study of natural phenomena. We cannot separate these two things: head and hand. An able hand, without a head to direct it, is a blind tool; the head is powerless without its executive hand.

[The steamboat] will answer for sea voyages as well as for inland navigation, in particular for packets, where there may be a great number of passengers. He is also of opinion, that fuel for a short voyage would not exceed the weight of water for a long one, and it would produce a constant supply of fresh water. ... [T]he boat would make head against the most violent tempests, and thereby escape the danger of a lee shore; and that the same force may be applied to a pump to free a leaky ship of her water. ... [T]he good effects of the machine, is the almost omnipotent force by which it is actuated, and the very simple, easy, and natural way by which the screws or paddles are turned to answer the purpose of oars.
[This letter was written in 1785, before the first steamboat carried a man (Fitch) on 27 Aug 1787.]