A Quote by Bertrand Russell
The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.
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The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
In this external world, which is full of finite things, it is impossible to see and find the Infinite. The Infinite must be sought in that alone which is infinite, and the only thing infinite about us is that which is within us, our own soul. Neither the body, nor the mind, nor even our thoughts, nor the world we see around us, is infinite.
The mathematical difficulties of the theory of rotation arise chiefly from the want of geometrical illustrations and sensible images, by which we might fix the results of analysis in our minds.
A modest critique of an age in which an actor is the President, in which fashion models are asked for their opinions, in which getting into a nightclub is seen as a significant human achievement.
We are a commercial people. We cannot boast of our arts, our crafts, our cultivation; our boast is in the wealth we produce. As a consequence business success is sanctified, and, practically, any methods which achieve it are justified by a larger and larger class.
If I were asked to name, in one word, the pole star round which the mathematical firmament revolves, the central idea which pervades the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this, it is this!
I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.
Farmers, merchants, manufacturers, and the traveling public have all had their troubles with the transportation lines, and the difficulties to which these struggles have given rise have produced that problem which is even now apparently far from solution.
Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.
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.
The mathematical is that evident aspect of things within which we are always already moving and according to which we experience them as things at all, and as such things. The mathematical is this fundamental position we take toward things by which we take up things as already given to us, and as they must and should be given. Therefore, the mathematical is the fundamental presupposition of the knowledge of things.
The greatest problem for the human species, the solution of which nature compels him to seek, is that of attaining a civil society which can administer justice universally.
Programmers are always surrounded by complexity; we cannot avoid it.... If our basic tool, the language in which we design and code our programs, is also complicated, the language itself becomes part of the problem rather than part of its solution.
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.
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