…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.

Already the steam-engine works our mines, impels our ships, excavates our ports and our rivers, forges iron, fashions wood, grinds grain, spins and weaves our cloths, transports the heaviest burdens, etc. It appears that it must some day serve as a universal motor, and be substituted for animal power, waterfalls, and air currents.

But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.

I have always considered that the substitution of the internal combustion engine for the horse marked a very gloomy milestone in the progress of mankind.

I have considered the two terms you want to substitute for eisode and exode, and upon the whole I am disposed to recommend instead of them anode and cathode. These words may signify eastern and western way, just as well as the longer compounds which you mention … I may mention too that anodos and cathodos are good, genuine Greek words, and not compounds coined for the purpose.

I was an impostor, the worthy associate of a brigand, &c., &c., and all this for an atom of chlorine put in the place of an atom of hydrogen, for the simple correction of a chemical formula!

In our century the conceptions substitution and substitution group, transformation and transformation group, operation and operation group, invariant, differential invariant and differential parameter, appear more and more clearly as the most important conceptions of mathematics.

Kepler’s suggestion of gravitation with the inverse distance, and Bouillaud’s proposed substitution of the inverse square of the distance, are things which Newton knew better than his modern readers. I have discovered two anagrams on his name, which are quite conclusive: the notion of gravitation was not new; but Newton went on.

Mathematics, the science of the ideal, becomes the means of investigating, understanding and making known the world of the real. The complex is expressed in terms of the simple. From one point of view mathematics may be defined as the science of successive substitutions of simpler concepts for more complex.

Science is now the craft of the manipulation, substitution and deflection of the forces of nature. What I see coming is a gigantic slaughterhouse, an Auschwitz, in which valuable enzymes, hormones, and so on will be extracted instead of gold teeth.

The difference between a successful and an unsuccessful business man lies often in the greater accuracy of the former’s guesses. Statistics are no substitution for judgment. Their use is to check and discipline the judgments on which in the last resort business decisions depend.

The essential molecule of reproduction, DNA, … is composed of only four nitrogen bases (adenine, thymine, guanine, and cytosine), the sugar deoxyribose, and a phosphate. DNA’s intermediary, RNA, differs only by the substitution of the sugar ribose for deoxyribose and the nitrogen base uracil for thymine. The proteins of living organisms are made with a mere 20 amino acids, all arranged in a “left-handed” configuration. Taking into account all 28 building blocks, or “letters” (20 amino acids, five bases, two sugars, and one phosphate), the message is clear: With such a limited alphabet, all life must have had a common chemical origin.

The law of conservation rigidly excludes both creation and annihilation. Waves may change to ripples, and ripples to waves,—magnitude may be substituted for number, and number for magnitude,—asteroids may aggregate to suns, suns may resolve themselves into florae and faunae, and florae and faunae melt in air,—the flux of power is eternally the same. It rolls in music through the ages, and all terrestrial energy,—the manifestations of life, as well as the display of phenomena, are but the modulations of its rhythm.

The mathematics of the twenty-first century may be very different from our own; perhaps the schoolboy will begin algebra with the theory of substitution groups, as he might now but for inherited habits.

The Post Office Committee of the House has referred to a sub-committee all the bills authorizing the building or buying of telegraph lines for the purpose of establishing a postal telegraph—that is, of sending mails by electricity … All is done by contract … with the carriage of mails by steam power [railroads] … It does not appear why there should be any difference of principle because of the substitution of electricity for steam.
[Foreshadowing email.]

Who does not know Maxwell’s dynamic theory of gases? At first there is the majestic development of the variations of velocities, then enter from one side the equations of condition and from the other the equations of central motions, higher and higher surges the chaos of formulas, suddenly four words burst forth: “Put n = 5.” The evil demon V disappears like the sudden ceasing of the basso parts in music, which hitherto wildly permeated the piece; what before seemed beyond control is now ordered as by magic. There is no time to state why this or that substitution was made, he who cannot feel the reason may as well lay the book aside; Maxwell is no program-musician who explains the notes of his composition. Forthwith the formulas yield obediently result after result, until the temperature-equilibrium of a heavy gas is reached as a surprising final climax and the curtain drops.