… the three positive characteristics that distinguish mathematical knowledge from other knowledge … may be briefly expressed as follows: first, mathematical knowledge bears more distinctly the imprint of truth on all its results than any other kind of knowledge; secondly, it is always a sure preliminary step to the attainment of other correct knowledge; thirdly, it has no need of other knowledge.

Il n'y a qu'un demi-siècle, un orateur chrétien, se défiant des hommes de la science leur disait: 'Arrêtez-vous enfin, et ne creusez pas jusqu'aux enfers.' Aujourd'hui, Messieurs, rassurés sur l'inébranlable constance de notre foi, nous vous disons: creusez, creusez encore; plus vous descendrez, plus vous rapprocherez du grand mystère de l'impuissance de l'homme et de la vérité de la religion. Creusez donc, creusez toujours,mundum tradidit disputationibus eorum; et quand la science aura donné son dernier coup de marteau sur les fondements de la terre, vous pourrez à la lueur du feu qu'il fera jaillir, lire encore l'idée de Dieu et contempler l'empreinte de sa main.
Only a half-century ago, a Christian speaker, mistrustful of men of science told them: 'Stop finally, and do not dig to hell.' Today, gentlemen, reassured about the steadfastness of our unshakeable faith, we say: dig, dig again; the further down you, the closer you come to the great mystery of the impotence of man and truth of religion. So dig, always dig: and when science has stuck its final hammer blow on the bosom of the earth, you will be able to ignite a burst of light, read furthermore the mind of God and contemplate the imprint of His hand.

By far the most important books for geology students were the quarries and clay pits, the cliffs and creek beds, the road and railroad cuts in woods and fields. Our words and letters were the imprints of plants and animals in stone, the minerals and crystals, and our vast, inexhaustible, incorruptible, and infallible library was nature itself.

I do not maintain that the chief value of the study of arithmetic consists in the lessons of morality that arise from this study. I claim only that, to be impressed from day to day, that there is something that is right as an answer to the questions with which one is able to grapple, and that there is a wrong answer—that there are ways in which the right answer can be established as right, that these ways automatically reject error and slovenliness, and that the learner is able himself to manipulate these ways and to arrive at the establishment of the true as opposed to the untrue, this relentless hewing to the line and stopping at the line, must color distinctly the thought life of the pupil with more than a tinge of morality. … To be neighborly with truth, to feel one’s self somewhat facile in ways of recognizing and establishing what is right, what is correct, to find the wrong persistently and unfailingly rejected as of no value, to feel that one can apply these ways for himself, that one can think and work independently, have a real, a positive, and a purifying effect upon moral character. They are the quiet, steady undertones of the work that always appeal to the learner for the sanction of his best judgment, and these are the really significant matters in school work. It is not the noise and bluster, not even the dramatics or the polemics from the teacher’s desk, that abide longest and leave the deepest and stablest imprint upon character. It is these still, small voices that speak unmistakably for the right and against the wrong and the erroneous that really form human character. When the school subjects are arranged on the basis of the degree to which they contribute to the moral upbuilding of human character good arithmetic will be well up the list.

Scientists have been only too willing to show their haughty disregard for philosophy. It is also true that in going against the practices of one’s own time and in ignoring the fashion prevailing in the schools and in books, one runs the risk of being very poorly received. But, after all, each philosopher works in his own way, and each brings to his philosophical speculations the imprint of his other studies and the turn of mind which they have given him. The theologian, the jurist, the mathematician, the physicist, and the philologist can each be recognised at a glance by the way in which he wears the mantle of philosophy.

Statistical accounts are to be referred to as a dictionary by men of riper years, and by young men as a grammar, to teach them the relations and proportions of different statistical subjects, and to imprint them on the mind at a time when the memory is capable of being impressed in a lasting and durable manner, thereby laying the foundation for accurate and valuable knowledge.