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“Christianity is realistic because it says that if there is no truth, there is also no hope; and there can be no truth if there is no adequate base. It is prepared to face the consequences of being proved false and say with Paul: If you find the body of Christ, the discussion is finished, let us eat and drink for tomorrow we die. It leaves absolutely no room for a romantic answer.”

“It is the invariable habit of bureaucracies, at all times and everywhere, to assume...that every citizen is a criminal. Their one apparent purpose, pursued with a relentless and furious diligence, is to convert the assumption into a fact. They hunt endlessly for proofs, and, when proofs are lacking, for mere suspicions. The moment they become aware of a definite citizen, John Doe, seeking what is his right under the law, they begin searching feverishly for an excuse for withholding it from him.”

“Make yourselves nests of pleasant thoughts. None of us knows what fairy palaces we may build of beautiful thought-proof against all adversity. Bright fancies, satisfied memories, noble histories, faithful sayings, treasure houses of precious and restful thoughts, which care cannot disturb, nor pain make gloomy, nor poverty take away from us.”

“Savings represent much more than mere money value. They are the proof that the saver is worth something in himself. Any fool can waste; any fool can muddle; but it takes something more of a man to save and the more he saves the more of a man he makes of himself. Waste and extravagance unsettle a man's mind for every crisis; thrift, which means some form of self-restraint, steadies it.”

“Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.”

“At one year of age the child says his first intentional wordhis babbling has a purpose, and this intention is a proof of conscious intelligenceHe becomes ever more aware that language refers to his surroundings, and his wish to master it consciously becomes also greater.Subconsciously and unaided, he strains himself to learn, and this effort makes his success all the more astonishing.”

“Pain, I came to feel, might well prove to be the sole proof of the persistence of consciousness within the flesh, the sole physical expression of consciousness. As my body acquired muscle, and in turn strength, there was gradually born within me a tendency towards the positive acceptance of pain, and my interest in physical suffering deepened.”

“Ask for a valiant heart which has banished the fear of death, which looks upon length of days as one of the least of nature's gifts; which is able to suffer every kind of hardship, is proof against anger, craves for nothing, and reckons the trials and gruelling labours of Hercules as more desirable blessings than the amorous ease and the banquets and cushions of Sardanapallus. The things that I recommend you can grant to yourself.”

“There is no proof. There are no authorities whatever. No president, Academy, Court of Law, Congress or Senate on this earth has the knowledge or power to decide what will be the knowledge of tomorrow. There is no use in trying to prove something that is unknown to somebody who is ignorant of the unknown, or fearful of its threatening power. Only the good old rules of learning will eventually bring about understanding of what has invaded our earthly existence.”

“The self-fulfilling prophecy is, in the beginning, a false definition of the situation evoking a new behavior which makes the originally false conception come true. The specious validity of the self-fulfilling prophecy perpetuates a reign of error. For the prophet will cite the actual course of events as proof that he was right from the very beginning.”

“The conspiracy community regularly seizes on one slip of the tongue, misunderstanding, or slight discrepancy to defeat twenty pieces of solid evidence; accepts one witness of theirs, even if he or she is a provable nut, as being far more credible than ten normal witnesses on the other side; treats rumors, even questions, as the equivalent of proof; leaps from the most minuscule of discoveries to the grandest of conclusions; and insists that the failure to explain everything perfectly negates all that is explained.”

“None of us can be proof against the influences that proceed from the persons he associates with. Wherefore, in books and men, let us look out for the best society, that which yields a bracing and wholesome influence. We all know the person for whose company we are the better, though the talk is only about fishing or embroidery.”

“Children, by nature, are keen, passionate and curious. What was referred to as laziness is often merely an awakening of sensitivity, a psychological inability to submit to certain absurd duties, and a natural result of the distorted, unbalanced education given to them. This laziness, which leads to an insuperable reluctance to learn, is, contrary to appearances, sometimes proof of intellectual superiority and a condemnation of the teacher.”

“Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.”

“Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.”

“What signifies protesting so against flattery when a person speaks well of one, it must either be true or false, you know if true, let us rejoice in his good opinion if he lies, it is a proof at least that he loves more to please me, than to sit s”

“On the Russian revolutionaries:To leave your parents, faithful and loyal subjects of the Emperor, to leave your profession, to desist from having children, to lose your fortune, and to give up your civil honor, all for revolutionary conviction, makes for a league of more practical proof than any religious order.”