~~[Attributed, authorship undocumented]~~ Mathematical demonstrations are a logic of as much or more use, than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even in subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedaemonians seldom elected any new kings, but such as had some knowledge in the mathematics, imagining those, who had not, men of imperfect judgments, and unfit to rule and govern.

A person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings, and aspirations to which he clings because of their superpersonal value. It seems to me that what is important is the force of this superpersonal content and the depth of the conviction concerning its overpowering meaningfulness, regardless of whether any attempt is made to unite this content with a divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly, a religious person is devout in the sense that he has no doubt of the significance and loftiness of those superpersonal objects and goals which neither require nor are capable of rational foundation. They exist with the same necessity and matter-of-factness as he himself. In this sense religion is the age-old endeavor of mankind to become clearly and completely conscious of these values and goals and constantly to strengthen and extend their effect. If one conceives of religion and science according to these definitions then a conflict between them appears impossible. For science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary.

Because basic learning takes place so early—as…the classic musical South Pacific reminds us, “You've got to be taught before it’s too late, before you are six or seven or eight; you’ve got to be carefully taught,”—we must strengthen our pre-school program, especially Headstart, Kindergarten and Day Care.

Character cannot be developed in ease and quiet. Only through experience of trial and suffering can the soul be strengthened, ambition inspired, and success achieved.

Every mathematical book that is worth reading must be read “backwards and forwards”, if I may use the expression. I would modify Lagrange’s advice a little and say, “Go on, but often return to strengthen your faith.” When you come on a hard or dreary passage, pass it over; and come back to it after you have seen its importance or found the need for it further on.

Exercise in the most rigorous thinking that is possible will of its own accord strengthen the sense of truth and right, for each advance in the ability to distinguish between correct and false thoughts, each habit making for rigour in thought development will increase in the sound pupil the ability and the wish to ascertain what is right in life and to defend it.

Great men stand like solitary towers in the city of God, and secret passages running deep beneath external nature give their thoughts intercourse with higher intelligences, which strengthens and consoles them, and of which the labourers on the surface do not even dream!

I pray every day and I think everybody should. I don’t think you can be up here and look out the window as I did the first day and look out at the Earth from this vantage point. We’re not so high compared to people who went to the moon and back. But to look out at this kind of creation out here and not believe in God is, to me, impossible. It just strengthens my faith.

In general … science per se does not increase the destructiveness of war, since, as a rule, it strengthens the defense as much as the attack.

Indeed, the aim of teaching [mathematics] should be rather to strengthen his [the pupil’s] faculties, and to supply a method of reasoning applicable to other subjects, than to furnish him with an instrument for solving practical problems.

It hath been an old remark, that Geometry is an excellent Logic. And it must be owned that when the definitions are clear; when the postulata cannot be refused, nor the axioms denied; when from the distinct contemplation and comparison of figures, their properties are derived, by a perpetual well-connected chain of consequences, the objects being still kept in view, and the attention ever fixed upon them; there is acquired a habit of reasoning, close and exact and methodical; which habit strengthens and sharpens the mind, and being transferred to other subjects is of general use in the inquiry after truth.

Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind.

Reaching the Moon by three-man vessels in one long bound from Earth is like casting a thin thread across space. The main effort, in the coming decades, will be to strengthen this thread; to make it a cord, a cable, and, finally, a broad highway.

Remember a networked learning machine’s most basic rule: strengthen the connections to those who succeed, weaken them to those who fail.

Since men are really interested in nothing but their own opinions, every one who puts forward an opinion looks about him right and left for means of strengthening himself and others in it.

The brain that isn’t used rusts. The brain that is used responds. The brain is exactly like any other part of the body: it can be strengthened by proper exercise, by proper use. Put your arm in a sling and keep it there for a considerable length of time, and, when you take it out, you find that you can’t use it. In the same way, the brain that isn’t used suffers atrophy.

The game of Chess is not merely an idle amusement. Several very valuable qualities of the mind, useful in the course of human life, are to be acquired or strengthened by it so as to become habits ready on all occasions.

The hostility of the state would be assured toward any system or science that might not strengthen its arm.

The metaphysical philosopher from his point of view recognizes mathematics as an instrument of education, which strengthens the power of attention, develops the sense of order and the faculty of construction, and enables the mind to grasp under the simple formulae the quantitative differences of physical phenomena.

The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.

This weapon [the atomic bomb] has added an additional responsibility—or, better, an additional incentive—to find a sound basis for lasting peace. It provides an overwhelming inducement for the avoidance of war. It emphasizes the crisis we face in international matters and strengthens the conviction that adequate safeguards for peace must be found.

We must make practice in thinking, or, in other words, the strengthening of reasoning power, the constant object of all teaching from infancy to adult age, no matter what may be the subject of instruction. … Effective training of the reasoning powers cannot be secured simply by choosing this subject or that for study. The method of study and the aim in studying are the all-important things.

What friends do with us and for us is a real part of our life; for it strengthens and advances our personality. The assault of our enemies is not part of our life ; it is only part of our experience ; we throw it off and guard ourselves against it as against frost, storm, rain, hail, or any other of the external evils which may be expected to happen.

What is education? Teaching a man what his powers and relations are, and how he can best extend, strengthen, and employ them.

Whatever advantage can be attributed to logic in directing and strengthening the action of the understanding is found in a higher degree in mathematical study, with the immense added advantage of a determinate subject, distinctly circumscribed, admitting of the utmost precision, and free from the danger which is inherent in all abstract logic—of leading to useless and puerile rules, or to vain ontological speculations. The positive method, being everywhere identical, is as much at home in the art of reasoning as anywhere else: and this is why no science, whether biology or any other, can offer any kind of reasoning, of which mathematics does not supply a simpler and purer counterpart. Thus, we are enabled to eliminate the only remaining portion of the old philosophy which could even appear to offer any real utility; the logical part, the value of which is irrevocably absorbed by mathematical science.