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.

By natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.

Engineering is the science and art of efficient dealing with materials and forces … it involves the most economic design and execution … assuring, when properly performed, the most advantageous combination of accuracy, safety, durability, speed, simplicity, efficiency, and economy possible for the conditions of design and service.

Every individual is continually exerting himself to find out the most advantageous employment for whatever capital he can command. It is his own advantage, indeed, and not that of society, which he has in view. But the study of his own advantage naturally, or rather necessarily, leads him to prefer that employment which is most advantageous to the society.

One geometry cannot be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.

Science and technology, and the various forms of art, all unite humanity in a single and interconnected system. As science progresses, the worldwide cooperation of scientists and technologists becomes more and more of a special and distinct intellectual community of friendship, in which, in place of antagonism, there is growing up a mutually advantageous sharing of work, a coordination of efforts, a common language for the exchange of information, and a solidarity, which are in many cases independent of the social and political differences of individual states.

The “British Association for the Promotion of Science,” … is almost necessary for the purposes of science. The periodical assemblage of persons, pursuing the same or différent branches of knowledge, always produces an excitement which is favourable to the development of new ideas; whilst the long period of repose which succeeds, is advantageous for the prosecution of the reasonings or the experiments then suggested; and the récurrence of the meeting in the succeeding year, will stimulate the activity of the inquirer, by the hope of being then enabled to produce the successful result of his labours.

The conflict of theories, leading, as it eventually must, to the survival of the fittest, is advantageous.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

Whatever plan of classification, founded on the natural relations of the elements, be adopted, in the practical study of chemistry, it will always be found most advantageous to commence with the consideration of the great constituents of the ocean and the atmosphere.