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“I HAVE no patience with the hypothesis occasionally expressed, and often implied, especially in tales written to teach children to be good, that babies are born pretty much alike, and that the sole agencies in creating differences between boy and boy, and man and man, are steady application and moral effort. It is in the most unqualified manner that I object to pretensions of natural equality. The experiences of the nursery, the school, the University, and of professional careers, are a chain of proofs to the contrary.”

“The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.”

“As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.”

“Superficial knowledge ... is hurtful to those who possess true genius; for it necessarily draws them away from their main object, wastes their industry over details and subjects foreign to their needs and natural talent, and lastly does not serve, as they flatter themselves, to prove the breadth of their mind. In all ages there have been men of very moderate intelligence who knew much, and so on the contrary, men of the highest intelligence who knew very little. Ignorance is not lack of intelligence, nor knowledge a proof of genius.”

“If the sewing societies, the avails of whose industry are now expended in supporting and educating young men for the ministry, were to withdraw their contributions to these objects, and give them where they are more needed, to their advancement of their own sex in useful learning, the next generation might furnish sufficient proof, that in intelligence and ability to master the whole circle of sciences, woman is not inferior to man.”

“Wisdom is not finally tested in schools, Wisdom cannot be pass'd from one having it to another not having it, Wisdom is of the soul, is not susceptible of proof, is its own proof, Applies to all stages and objects and qualities and is content, Is the certainty of the reality and immortality of things, and the excellence of things; Something there is in the float of the sight of things that provokes it out of the soul.”

“I do object to the assumption that anything that might be outside of nature is ruled out of the conversation. That's an impoverished view of the kinds of questions we humans can ask, such as "Why am I here?", "What happens after we die?", "Is there a God?" If you refuse to acknowledge their appropriateness, you end up with a zero probability of God after examining the natural world because it doesn't convince you on a proof basis.”