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A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy which defends the pursuit of mathematics for its own sake. Central to Hardy's "apology" – in the sense of a formal justification or defence (as in Plato's Apology of Socrates) – is an argument that mathematics has value independent of its applications.
G. H. Hardy is usually known by those outside the field of mathematics for his 1940 essay A Mathematician's Apology, often considered one of the best insights into the mind of a working mathematician written for the layperson.
In his 1940 essay A Mathematician's Apology, G. H. Hardy suggested that a beautiful proof or result possesses "inevitability", "unexpectedness", and "economy". [9] In 1997, Gian-Carlo Rota, disagreed with unexpectedness as a sufficient condition for beauty and proposed a counterexample:
G. H. Hardy, A Mathematician's Apology (1940) [1] He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one.
Mathematicians have always had differing opinions regarding the distinction between pure and applied mathematics. One of the most famous (but perhaps misunderstood) modern examples of this debate can be found in G.H. Hardy's 1940 essay A Mathematician's Apology. It is widely believed that Hardy considered applied mathematics to be ugly and dull.
A Mathematician's Apology - G.H. Hardy [16] A Mathematician's Miscellany (republished as Littlewood's miscellany) - J. E. Littlewood [17] I Am a Mathematician - Norbert Wiener [18] I Want to be a Mathematician - Paul R. Halmos; Adventures of a Mathematician - Stanislaw Ulam [19] Enigmas of Chance - Mark Kac [20] Random Curves - Neal Koblitz
Apology, Xenophon's version of Socrates' defense; A Mathematician's Apology (1940), an essay by British mathematician G. H. Hardy; Apologeticus or Apology (c. AD 197) of Tertullian; Apologia Pro Vita Sua (1864), a defense of Catholicism by John Henry Newman; Apology of the Augsburg Confession (1531), a defense of Lutheranism by Philipp Melanchthon
In A Mathematician's Apology, G. H. Hardy criticized Rouse Ball for including this problem, writing: "These are odd facts, very suitable for puzzle columns and likely to amuse amateurs, but there is nothing in them which appeals to a mathematician. The proofs are neither difficult nor interesting—merely tiresome.