Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
In general, I'm in support of promoting art and science in public schools. I think music and science are probably the most important factors for the human brain developing. Even more so than any other fields, because music covers mathematics, cognitive reasoning, motor skills, coordination, like, it's kind of everything.
Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.
I could never accept findings based almost exclusively on mathematics. It ain't ignorance that causes all the trouble in this world. It's the things people know that ain't so.
I had a feeling once about mathematics - that I saw it all... but it was after dinner and I let it go.
Mathematics is written for mathematicians.
...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
The word "art" means harmony for me. I never speak of mathematics and never bother with the Spirit. My only science is the choice of impressions that the light in the universe furnishes to my consciousness as an artisan which I try, by imposing an Order, and Art, an appropriate representative life, to organize.
You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.
Logic and mathematics are nothing but specialised linguistic structures.
Mathematics is less related to accounting than it is to philosophy.
So mathematical truth prefers simple words since the language of truth is itself simple.
Perhaps the most surprising thing about mathematics is that it is so surprising.
Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.
[Mathematics] is an independent world created out of pure intelligence.
Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
Music is what mathematics does on a Saturday night.
Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Life is a school of probability.
... preliminary accounting, banking and surveying (known as arithmetic, algebra and geometry).
When we were making the law, when we were writing the literature and the mathematics the grandfarthers of Blair and little Bush were scratching around in caves.
Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.
You know we're constantly taking. We don't make most of the food we eat, we don't grow it, anyway. We wear clothes other people make, we speak a language other people developed, we use a mathematics other people evolved and spent their lives building. I mean we're constantly taking things. It's a wonderful ecstatic feeling to create something and put it into the pool of human experience and knowledge.
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