“We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for… [The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for.”

—  Hermann Weyl

The Mathematical Way of Thinking (1941)

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Hermann Weyl 28
German mathematician 1885–1955

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S. I. Hayakawa photo

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“Purely mathematical symbols have no meaning by themselves; it is the privilege of pure mathematicians, to quote Bertrand Russell, not to know what they are talking about. …It is the physicist, and not the mathematician, who must know what he is talking about.”

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“It remains a real world if there is a background to the symbols — an unknown quantity which the mathematical symbol x stands for. We think we are not wholly cut off from this background. It is to this background that our own personality and consciousness belong, and those spiritual aspects of our nature not to be described by any symbolism … to which mathematical physics has hitherto restricted itself.”

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R. G. Collingwood (1889–1943) British historian and philosopher

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Arthur Stanley Eddington (1882–1944) British astrophysicist

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L. E. J. Brouwer photo

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as translated by Arnold Dresden from: Brouwer, L. E. J. (1913). Intuitionism and formalism. Bulletin of the American Mathematical Society, 20(2), 81–96. (quote on p. 84)

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S. I. Hayakawa photo

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S. I. Hayakawa book Language in Thought and Action

See also: The Meaning of Meaning (1923)
See also: Science and Sanity (1933)
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