If you had done something twice, you are likely to do it again.
It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.
And for mathematical science, he that doubts their certainty hath need of a dose of hellebore.
The very term 'combinatorial methods' has an oxymoronic character.
Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.
. . . 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.
Counting pairs is the oldest trick in combinatorics... Every time we count pairs, we learn something from it.
Mathematical Mark all mathematical heads, which be only and wholly bent to those sciences, how solitary they be themselves, how unfit to live with others, and how unapt to serve in the world.
I don't agree with mathematics; the sum total of zeros is a frightening figure.
Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.
With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.
Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity
I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming . . . and a little mad.
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.
Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
Mathematics is a collection of cheap tricks and dirty jokes.
Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.
When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.
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.
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.
All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty. They give me no pleasure. They are merely auxiliaries. At close range it is all not true.
Life is an offensive, directed against the repetitious mechanism of the Universe.
There are two types of mind . . . the mathematical, and what might be called the intuitive. The former arrives at its views slowly, but they are firm and rigid; the latter is endowed with greater flexibility and applies itself simultaneously to the diverse lovable parts of that which it loves.
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