. . . She knew only that if she did or said thus-and-so, men would unerringly respond with the complimentary thus-and-so. It was like a mathematical formula and no more difficult, for mathematics was the one subject that had come easy to Scarlett in her schooldays.
Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.
It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.
If things are nice there is probably a good reason why they are nice: and if you do not know at least one reason for this good fortune, then you still have work to do.
Mathematics is a collection of cheap tricks and dirty jokes.
When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.
Counting pairs is the oldest trick in combinatorics... Every time we count pairs, we learn something from it.
If you had done something twice, you are likely to do it again.
Mathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be surprising if such a step has been found and lost again.
Everyone else would climb a peak by looking for a path somewhere in the mountain. Nash would climb another mountain altogether and from that distant peak would shine a searchlight back onto the first peak.
The very term 'combinatorial methods' has an oxymoronic character.
If you think it's simple, then you have misunderstood the problem.
I never use a computer.
When I entered graduate school I had carried out the instructions given to me by my father and had knocked on both Murray Gell-Mann's and Feynman's doors and asked them what they were currently doing. Murray wrote down the partition function for the three-dimensional Ising model and said it would be nice if I could solve it (at least that is how I remember the conversation). Feynman's answer was 'nothing'.
Numbers are intellectual witnesses that belong only to mankind.
I don't agree with mathematics; the sum total of zeros is a frightening figure.
[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.
With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.
Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.
It is not enough to have a good mind. The main thing is to use it well.
To speak algebraically, Mr. M. is execrable, but Mr. G. is (x + 1)- ecrable.
An unsophisticated forecaster uses statistics as a drunken man uses lamp-posts - for support rather than for illumination.
USA Today has come out with a new survey - apparently, three out of every four people make up 75% of the population.
Life is an offensive, directed against the repetitious mechanism of the Universe.
The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.
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