And for mathematical science, he that doubts their certainty hath need of a dose of hellebore.
I do not think we are ever going to be able to, for a long time, get the kind of quality of school personnel that we need in our schools, especially in the areas of science and math. One of the answers to that problem is to use more educational technology.
You live your life between your ears.
All the math you need in the stock market you get in the fourth grade.
Desire animates the world. It is present in the baby crying for milk, the girl struggling to solve a math problem, the woman running to meet her lover and later deciding to have children, and the old woman, hunched over her walker, moving down the hall of the nursing home at a glacial pace to pick up her mail. Banish desire from the world, and you get a world of frozen beings who have no reason to live and no reason to die.
Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.
It is the story that matters, not just the ending.
Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.
... if one were to refuse to have direct, geometric, intuitive insights, if one were reduced to pure logic, which does not permit a choice among every thing that is exact, one would hardly think of many questions, and certain notions ... would escape us completely.
If one must choose between rigour and meaning, I shall unhesitatingly choose the latter.
What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises.
The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding, are known only to him who has experienced them himself.
... commutative algebra is a lot like topology, only backwards.
Geometry is the art of correct reasoning from incorrectly drawn figures.
All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.
Topology is precisely the mathematical discipline that allows the passage from local to global.
There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.
The electron is a theory we use; it is so useful in understanding the way nature works that we can almost call it real.
Although this may seem a paradox, all exact science is based on the idea of approximation. If a man tells you he knows a thing exactly, then you can be safe in inferring that you are speaking to an inexact man.
Quadratic reciprocity is the song of love in the land of prime numbers.
Why do I act as I do? To tell you the truth, I have absolutely no idea why. It is simply my nature to act as I act, and that's all I can say.
Sticks and stones may break my bones, but words can make me think I deserved it.
It is not only the prisoners who grow coarse and hardened from corporal punishment, but those as well who perpetrate the act or are present to witness it.
There are no solved problems; there are only problems that are more or less solved.
Only professional mathematicians learn anything from proofs. Other people learn from explanations.
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