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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.
A Mathematician's Apology. With a foreword by C. P. Snow. Cambridge: Cambridge University Press. ISBN 978-1-107-29559-9. Full text The reprinted Mathematician's Apology with an introduction by C.P. Snow was recommended by Marcus du Sautoy in the BBC Radio program A Good Read in 2007. [40] Hardy, G. H. (1999) [1st pub. Cambridge University Press ...
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:
Mathematician Pham Huu Tiep and his colleagues have made a proof of one longstanding open problem and one additional foundational question in a subfield of abstract algebra known as representation ...
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.
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Borwein's paper has a section on Gauss, Hadamard and Hardy, and in subsection 2.3 he describes Hardy as a "stylish author who wrote compellingly in defense of pure mathematics". He calls Hardy's Apology a "spirited defense of beauty over utility". After these words of praise, Borwein adds a single critical comment:
A good apology starts with the willingness to listen and hear what the injured party has to say despite any objections you may have. “Sit in the hot seat and listen with an open heart to the ...