By these pleasures it is permitted to relax the mind with play, in turmoils of the mind, or when our labors are light, or in great tension, or as a method of passing the time. A reliable witness is Cicero, when he says (De Oratore, 2): 'men who are accustomed to hard daily toil, when by reason of the weather they are kept from their work, betake themselves to playing with a ball, or with knucklebones or with dice, or they may also contrive for themselves some new game at their leisure.'

Euler was a believer in God, downright and straightforward. The following story is told by Thiebault, in his Souvenirs de vingt ans de séjour à Berlin, … Thiebault says that he has no personal knowledge of the truth of the story, but that it was believed throughout the whole of the north of Europe. Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her counsellors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced toward Diderot, and said gravely, and in a tone of perfect conviction:
Monsieur, (a + bⁿ) / n = x, donc Dieu existe; repondez!
Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.

From man or angel the great Architect did wisely to conceal, and not divulge his secrets to be scanned by them who ought rather admire; or if they list to try conjecture, he his fabric of the heavens left to their disputes, perhaps to move his laughter at their quaint opinions wide hereafter, when they come to model heaven calculate the stars, how they will wield the mighty frame, how build, unbuild, contrive to save appearances, how gird the sphere with centric and eccentric scribbled o’er, and epicycle, orb in orb.

Nature never “fails.” Nature complies with its own laws. Nature is the law. When Man lacks understanding of Nature’s laws and a Man-contrived structure buckles unexpectedly, it does not fail. It only demonstrates that Man did not understand Nature’s laws and behaviors. Nothing failed. Man’s knowledge or estimating was inadequate.

Only a people serving an apprenticeship to nature can be trusted with machines. Only such people will so contrive and control those machines that their products are an enhancement of biological needs, and not a denial of them.

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.

Scientific theory is a contrived foothold in the chaos of living phenomena.

The subsequent course of nature, teaches, that God, indeed, gave motion to matter; but that, in the beginning, he so guided the various motion of the parts of it, as to contrive them into the world he design'd they should compose; and establish'd those rules of motion, and that order amongst things corporeal, which we call the laws of nature. Thus, the universe being once fram'd by God, and the laws of motion settled, and all upheld by his perpetual concourse, and general providence; the same philosophy teaches, that the phenomena of the world, are physically produced by the mechanical properties of the parts of matter; and, that they operate upon one another according to mechanical laws. 'Tis of this kind of corpuscular philosophy, that I speak.

These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.

You may perceive something of the distinction which I think necessary to keep in view between art and science, between the artist and the man of knowledge, or the philosopher. The man of knowledge, the philosopher, is he who studies and acquires knowledge in order to improve his own mind; and with a desire of extending the department of knowledge to which he turns his attention, or to render it useful to the world, by discoveries, or by inventions, which may be the foundation of new arts, or of improvements in those already established. Excited by one or more of these motives, the philosopher employs himself in acquiring knowledge and in communicating it. The artist only executes and practises what the philosopher or man of invention has discovered or contrived, while the business of the trader is to retail the productions of the artist, exchange some of them for others, and transport them to distant places for that purpose.