Mathematics Is a Language

The notion that Mathematics is a language is held by many mathematicians and is being expressed on frequent occasions. Below, I am going to collect quotes I occasionally come across that uphold that point.

  1. R. L. E. Schwarzenberger, The Language of Geometry, in A Mathematical Spectrum Miscellany, Applied Probability Trust, 2000, p. 112:

    My own attitude, which I share with many of my colleagues, is simply that mathematics is a language. Like English, or Latin, or Chinese, there are certain concepts for which mathematics is particularly well suited: it would be as foolish to attempt to write a love poem in the language of mathematics as to prove the Fundamental Theorem of Algebra using the English language.

  2. Yu. Manin, Mathematics as profession and vocation, in Mathematics: Frontiers and Perspectives, (V. Arnold et al, ed), AMS, 200, p. 154:

    The basis of all human culture is language, and mathematics is a special kind of linguistic activity.

  3. A. Adler, Mathematics and Creativity, in The World Treasury of Physics, Astronomy and Mathematics, (T. Ferris, ed), Little, Brown and Co, 1991, p. 435:

    Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. (In a spoken language, there exist words, like "happiness", that defy definition.) It is also an art - the most intellectual and classical of the arts.

  4. J.-P. Changeux, A. Connes, Conversations on Mind, Matter and Mathematics, Princeton University Press, 1995, p. 10:

    Changeux: Mathematical language is plainly an authentic language. But is it therefore the only authentic language?

    Connes: It is unquestionably the only universal language.

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