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Hardy defined a set of criteria for mathematical beauty. In the book's title, Hardy uses the word " apology " in the sense of a formal justification or defence as in Plato 's Apology of Socratesnot in the sense of a plea for forgiveness. Hardy felt the need to justify his life's work in mathematics at this time mainly for two reasons.
Firstly, at age 62, Hardy felt the approach of old age he had survived a heart attack in and the decline of his mathematical creativity and skills.
By devoting time to writing the Apology, Hardy was admitting that his own time as a creative mathematician was finished. In his foreword to the edition of the book, C. Snow describes the Apology as "a passionate lament for creative powers that used to be and that will never come again".
In Hardy's words, "Exposition, criticism, appreciation, is work for second-rate minds. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.
He wanted to write a book in which he would explain his mathematical philosophy to the next generation of mathematicians; that would defend mathematics by elaborating on the merits of pure mathematics solely, without having to resort to the attainments of applied mathematics in order to justify the overall importance of mathematics; and that would inspire the upcoming generations of pure mathematicians.
Hardy was an atheistand makes his justification not to God but to his fellow man.
One of the main themes of the book is the beauty that mathematics possesses, which Hardy compares to painting and poetry. Hardy contends that if useful knowledge is defined as knowledge which is likely to contribute to the material comfort of mankind in the near future if not right nowso that mere intellectual satisfaction is irrelevant, then the great bulk of higher mathematics is useless.
He justifies the pursuit of pure mathematics with the argument that its very "uselessness" on the whole meant that it could not be misused to cause harm. On the other hand, Hardy denigrates much of the applied mathematics as either being "trivial", "ugly", or "dull", and contrasts it with "real mathematics", which is how he ranks the higher, pure mathematics.
Hardy expounds by commenting about a phrase attributed to Carl Friedrich Gauss that "Mathematics is the queen of the sciences and number theory is the queen of mathematics. If an application of number theory were to be found, then certainly no one would try to dethrone the "queen of mathematics" because of that.
What Gauss meant, according to Hardy, is that the underlying concepts that constitute number theory are deeper and more elegant compared to those of any other branch of mathematics. Another theme is that mathematics is a "young man's game", so anyone with a talent for mathematics should develop and use that talent while they are young, before their ability to create original mathematics starts to decline in middle age.
This view reflects Hardy's increasing depression at the wane of his own mathematical powers. For Hardy, real mathematics was essentially a creative activity, rather than an explanatory or expository one.A Mathematician's Apology is a essay by British mathematician G.
H. monstermanfilm.com concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician.
This is supposedly an actual essay written by an extremely creative college applicant to NYU. The author was accepted and is reportedly now attending NYU. In Contravention of Conventional Wisdom CIA “no touch” torture makes sense out of mind control allegations By Cheryl Welsh January Also available as a pdf.
Cheryl Welsh was invited to speak about mind control allegations at a recent workshop on ethics and interrogations by the workshop director, Jean Maria Arrigo PhD.
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