A Quote by Albert Einstein
Pure mathematics is, in its way, the poetry of logical ideas. ... [By seeking] logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.
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Pure mathematics is, in its way, the poetry of logical ideas.
If you let your mind talk you out of things that aren't logical, you're going to have a very boring life. Because grace isn't logical. Love isn't logical. Miracles aren't logical.
Poetry has an indirect way of hinting at things. Poetry is feminine. Prose is masculine. Prose, the very structure of it, is logical; poetry is basically illogical. Prose has to be clear-cut; poetry has to be vague - that's its beauty, its quality. Prose simply says what it says; poetry says many things. Prose is needed in the day-to-day world, in the marketplace. But whenever something of the heart has to be said, prose is always found inadequate - one has to fall back to poetry.
The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them.
[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.
To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.
It is not logical for art to be logical. Art goes against the grain of the times as readily as it goes with it and at the very same moment. Instead of seeking the nearest exit, art responds to a new situation by uncovering a labyrinth of problems.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the georgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
As soon as a thought or word becomes a tool, one can dispense with actually 'thinking' it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of mathematics - the model of all neo-positivistic thinking - lies in just this 'intellectual economy.' Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based. ... Reason ... becomes a fetish, a magic entity that is accepted rather than intellectually experienced.
We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.
My advice is not always so logical and consistent. But then, love is not logical and consistent. So why should my advice be? If you want that kind of thinking, go to a computer. Computers are always logical and consistent, and you see how often they get proposed to.
Logical activity is not the whole of intelligence. One can be intelligent without being particularly logical.
It is always easy to be logical. It is almost impossible to be logical to the bitter end.
"Who are we to say what is right and what is wrong?" is the common refrain under the doctrine of pure pluralism. Clearly, society cannot long survive if this principle is pushed to its logical conclusion and everyone is free to write his own laws.
There is no logical way to the discovery of these elemental laws. There is only the way of intuition, which is helped by a feeling for the order lying behind the appearance.
To exist (in mathematics), said Henri Poincaré, is to be free from contradiction. But mere existence does not guarantee survival. To survive in mathematics requires a kind of vitality that cannot be described in purely logical terms.
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