Mathematics Quotes
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As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
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Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.
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One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.
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Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.
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I went to Princeton from Amherst, where I split my interests between mathematics and philosophy.
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Sex is the mathematics urge sublimated.
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All creative people hate mathematics. It's the most uncreative subject you can study.
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Lisp ... made me aware that software could be close to executable mathematics.
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I fly in dreams, I know it is my privilege, I do not recall a single situation in dreams when I was unable to fly. To execute every sort of curve and angle with a light impulse, a flying mathematics - that is so distinct a happiness that it has permanently suffused my basic sense of happiness.
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It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.
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Irrefragability, thy name is mathematics.
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The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest, and he will succeed only if he presents things in a form intuitively comprehensible. A more abstract presentation is only possible in the upper classes.
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The creative principle of science resides in mathematics.
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Insofar as mathematics is true, it does not describe the real world. Insofar as it describes the real world, it is not true.
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Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
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Beyond the natural numbers, addition, multiplication, and mathematical induction are intuitively clear.
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It seems that every practitioner of physics has had to wonder at some point why mathematics and physics have come to be so closely entwined. Opinions vary on the answer. ..Bertrand Russell acknowledged..'Physics is mathematical not because we know so much about the physical world, but because we know so little.' ..Mathematics may be indispensable to physics, but it obviously does not constitute physics.
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The faith of scientists in the power and truth of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation.... But the facts which are accepted by virtue of these tests are not actually observed at all.
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If you want to be a physicist, you must do three things-first, study mathematics, second, study more mathematics, and third, do the same.
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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.
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For centuries, everything was taught through music. History was taught through music; language and mathematics were taught through music.
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Mathematics is written for mathematicians.
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In mathematics and science, there is no difference in the intelligence of men and women. The difference in genes between men and women is simply the Y chromosome, which has nothing to do with intelligence.
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Mathematics deals exclusively with the relations of concepts to each other without consideration of their relation to experience.
