[Before the time of Benjamin Peirce it never occurred to anyone that mathematical research] was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood alone—a mountain peak whose absolute height might be hard to measure, but which towered above all the surrounding country.

A noiseless, patient spider,
I mark’d, where on a little promontory, it stood, isolated;
Mark’d how, to explore the vacant, vast surrounding,
It launch’d forth filament, filament, filament, out of itself
Ever unreeling them—ever tirelessly speeding them.

I believe with Schopenhauer that one of the strongest motives that lead men to art and science is escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one’s own ever shifting desires. A finely tempered nature longs to escape from personal life into the world of objective perception and thought; this desire may be compared with the townsman’s irresistible longing to escape from his noisy, cramped surroundings into the silence of high mountains, where the eye ranges freely through the still, pure air and fondly traces out the restful contours apparently built for eternity.

If the Weismann idea triumphs, it will be in a sense a triumph of fatalism; for, according to it, while we may indefinitely improve the forces of our education and surroundings, and this civilizing nurture will improve the individuals of each generation, its actual effects will not be cumulative as regards the race itself, but only as regards the environment of the race; each new generation must start de novo, receiving no increment of the moral and intellectual advance made during the lifetime of its predecessors. It would follow that one deep, almost instinctive motive for a higher life would be removed if the race were only superficially benefited by its nurture, and the only possible channel of actual improvement were in the selection of the fittest chains of race plasma.

It is of priceless value to the human race to know that the sun will supply the needs of the earth, as to light and heat, for millions of years; that the stars are not lanterns hung out at night, but are suns like our own; and that numbers of them probably have planets revolving around them, perhaps in many cases with inhabitants adapted to the conditions existing there. In a sentence, the main purpose of the science is to learn the truth about the stellar universe; to increase human knowledge concerning our surroundings, and to widen the limits of intellectual life.

It is probable that serum acts on bacteria by changing the relations of molecular attraction between the bacteria and the surrounding fluid.

Science has “explained” nothing; the more we know the more fantastic the world becomes and the profounder the surrounding darkness.

Science is but a feeble means for motivating life. It enlightens men, but fails to arouse them to deeds of self-sacrifice and devotion. … It dispels ignorance, but it never launched a crusade. It gives aid in the struggle with the hard surroundings of life, but it does not inform us to what end we struggle, or whether the struggle is worth while. … Intelligence can do little more than direct.

So far from science being irreligious, as many think, it is the neglect of science that is irreligious—it is the refusal to study the surrounding creation that is irreligious.

Take the rose—most people think it very beautiful: I don’t care for it at all. I prefer the cactus, for the simple reason that it has a more interesting personality. It has wonderfully adapted itself to its surroundings! It is the best illustration of the theory of evolution in plant life.

The earliest signs of living things, announcing as they do a high complexity of organization, entirely exclude the hypothesis of a transmutation from lower to higher grades of being. The first fiat of Creation which went forth, doubtlessly ensured the perfect adaptation of animals to the surrounding media; and thus, whilst the geologist recognizes a beginning, he can see in the innumerable facts of the eye of the earliest crustacean, the same evidences of Omniscience as in the completion of the vertebrate form.

The growing complexity of civilized life demands with each age broader and more exact knowledge as to the material surroundings and greater precision in our recognition of the invisible forces or tendencies about us.

When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain’s sheer face, encountering obstacles at every turn, often retracing one’s steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding countryside and then noting the automobile road up the other side!