A Quote by George Boole
No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.
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The physicist may be satisfied when he has the mathematical scheme and knows how to use for the interpretation of the experiments. But he has to speak about his results also to non-physicists who will not be satisfied unless some explanation is given in plain language. Even for the physicist the description in plain language will be the criterion of the degree of understanding that has been reached.
Music, also, the architect ought to understand so that he may have knowledge of the canonical and mathematical theory, and besides be able to tune ballistae , catapultae, and scorpiones to the proper key. For to the right and left in the beams are the holes in the frames through which the strings of twisted sinew are stretched by means of windlasses and bars, and these strings must not be clamped and made fast until they give the same correct note to the ear of the skilled workman.
If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.
It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.
When we're dealing with the people in our family - no matter how annoying or gross they may be, no matter how self-inflicted their suffering may appear, no matter how afflicted they are with ignorance, prejudice or nose hairs - we give from the deepest parts of ourselves.
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
We must all learn to live together as brothers. Or we will all perish together as foolsFor some strange reason I can never be what I ought to be until you are what you ought to be. And you can never be what you ought to be until I am what I ought to be.
Delusion gives you more happiness than truth gives to me. For injuries ought to be done all at one time, so that, being tasted less, they offend less; benefits ought to be given little by little, so that the flavour of them may last longer.
But that the reasoning from these facts, the drawing from them correct conclusions, is a matter of great difficulty, may be inferred from the imperfect state in which the Science is now found after it has been so long and so intensely studied.
I think that if your tenure case depends on your proving what you thought was a mathematical theorem and the proposed theorem turns out to be false just before your tenure decision, and you want to get tenure very badly, there is a sense in which it's perfectly understandable and reasonable of you to wish the proposed theorem were true and provable, even if it's logically impossible for it to be.
The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.
The old order, it is good for the old. A farmer wants his son to be afraid of beautiful women, so that he will not leave home too soon, so he tells a story about how one drowned his brother’s cousin’s friend in a lake, not because he was a pig who deserved to be drowned, but because beautiful women are bad, and also witches. And it doesn’t matter that she didn’t ask to be beautiful, or to be born in a lake, or to live forever, or to not know how men breathe until they stop doing it.
You can be fully satisfied with where you are, understanding that you're eternally evolving. When you get into that place of feeling appreciation of where you are and of who you are, and appreciation of what you are, and you accept that you are a never-ending, always unfolding Being, then you can stand in that delicate balance of being optimistic about what is to come, without being unhappy about where you stand. Find a way of eagerly anticipating future changes, while at the same time you are in love and satisfied with who, what, where and how you be.
There is, of course, great value in belonging to a group. Safety in numbers, for one. But there is also a mathematical explanation for why the brain is so willing to give up its own opinions: a group of people is more likely to be correct about something than an individual.
The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.
In a real sense all life is inter-related. All men are caught in an inescapable network of mutuality, tied in a single garment of destiny. Whatever affects one directly, affects all indirectly. I can never be what I ought to be until you are what you ought to be, and you can never be what you ought to be until I am what I ought to be... This is the inter-related structure of reality.
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