There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.
How happy is the lot of the mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. No cashier writes a letter to the press complaining about the incomprehensibility of Modern Mathematics and comparing it unfavorably with the good old days when mathematicians were content to paper irregularly shaped rooms and fill bathtubs without closing the waste pipe.
Fifty percent of all doctors graduate in the bottom half of their class - Hope your surgery went well!
Two wrongs don't make a right.
Every moment dies a man, Every moment one is born.
I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.
Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
One man may have some special knowledge at first-hand about the character of a river or a spring, who otherwise knows only what everyone else knows. Yet to give currency to this shred of information, he will undertake to write on the whole science of physics. From this fault many great troubles spring.
Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavour does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.
A proposition of geometry does not compete with life; and a proposition of geometry is a fair and luminous parallel for a work of art. Both are reasonable, both untrue to the crude fact; both inhere in nature, neither represents it.
There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time ... On the other hand, I think I can safely say that nobody understands quantum mechanics.
You can see the meaning of the statement that "Literature is a living art" most easily and clearly, perhaps, by contrasting Science and Art at their two extremes - say Pure Mathematics and Acting. Science as a rule deals with things, Art with man's thought and emotion about things.
Cardinal arithmetic will be quite important for us, so we spend some time on it. Since, however, it tends to be trivial, we shall not need to spend much of this time on proofs.
Everybody who reasons carefully about anything is making a contribution ... and if you abstract it away and send it to the Department of Mathematics they put it in books.
Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room.
Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
I came to the ... open gate of mathematics. From here, well-trodden paths lead in every direction, and since then I have often spent time there. Sometimes I think ... I have trodden all the paths ... and then I suddenly discover a new path and experience fresh delights.
Wherefore in all great works are Clerks so much desired? Wherefore are Auditors so well-fed? What causeth Geometricians so highly to be enhaunsed? Why are Astronomers so greatly advanced? Because that by number such things they find, which else would farre excell mans minde.
In India, I learned a proverb that says, 'Distrust the calculation seven times over, the mathematician a hundred times.'
Strong Reason and good fancy, joyn'd with experience and tryalls, so that we are assured of the good effects of it.
We were to found a University magazine. A pair of little, active brothers-Livingstone by name, great skippers on the foot, great rubbers of the hands, who kept a book-shop over against the University building-had been debauched to play the part of publishers. We four were to be conjuct editors and, what was the main point of the concern, to print our own works; while, by every rule of arithmetic-that flatterer of credulity-the adventure must succeed and bring great profit. Well, well: it was a bright vision.
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