Mathematician's apology
A Mathematician's Apology (for example: "Defense speech of a mathematician" or "Apology of a mathematician") is an essay written in 1940 by the British mathematician Godfrey Harold Hardy . He deals with the aesthetics of mathematics, whereby he also allows personal information to flow in, and gives the layman insight into the world of thought of the mathematician at work.
Summary
In the title, Hardy uses the word " apology " in the sense of a justification or defense speech (such as Plato's apology of Socrates ) and not in the sense of a request for forgiveness. At 62, Hardy felt his advancing age (he had survived a heart attack in 1939 and could no longer play his usual tennis) and the fading of his mathematical creativity and skills. He suffered from depression, aggravated by the death of a close friend and the war. For these reasons, Hardy decided to display his fascination with mathematics and his life dedicated to mathematics. By writing the apology, Hardy admitted that his days as a creative mathematician had come to an end. C. P. Snow describes the apology in the foreword to the 1967 edition "as a passionate lament for a creative force that was once and will never be again."
In Hardy's words, presenting, criticizing and appreciating scientific work is an activity for second-rate scientists. It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The job of a mathematician is to create new theories, to contribute something new to mathematics, and not just to write about what he and other mathematicians have achieved. Second, Hardy, who was a committed pacifist , wanted to justify his opinion at the beginning of World War II that mathematics should be done for its own sake, not for its applicability. He wanted to write a book explaining his mathematical philosophy to the next generation of mathematicians; that would defend mathematics on the basis of its endogenous meaning, by working out pure mathematics alone, without resorting to the successes of applied mathematics to justify the general meaning of mathematics; and that would also inspire future generations of pure mathematicians. Since Hardy was an atheist , he does not justify himself to God , but only to his fellow men.
One of the main themes of the book is the beauty of mathematics, which Hardy compares to painting and poetry. The most beautiful mathematics for Hardy was pure mathematics that had no application in the outside world, especially his own special area, number theory . He justifies the pursuit of pure mathematics with the argument that its uselessness means that it can never be misused to cause harm. On the other hand, Hardy devalues applied mathematics . He describes them as "ugly", "trivial" and "boring". These applied math features do not mean that the math is "ugly," "trivial," and "boring" because it is applied, but that most of the time the ugliest, most trivial, and boring math is what can be applied.
Hardy explains a sentence that is attributed to Carl Friedrich Gauß : Hardy explains that "Mathematics is the queen of the sciences and number theory is the queen of mathematics". Some people believe that it was the extreme inapplicability of number theory that led Gauss to make the above statement about number theory. But Hardy said that this is certainly not the reason. If one found an application of number theory, then certainly nobody would try to dethrone "the queen of mathematics" because of it. What Gauss said, according to Hardy, is that the very concept of number theory is much deeper and more elegant compared to other branches of mathematics.
Another theme is the idea that math is a "young man's game". This means that all people who have a talent for math should develop and use it while they are young, before their ability to do original math begins to decline in middle age. This view reflects Hardy's growing depression about the decline in his own math skills. For Hardy, real math was actually more of a creative activity than an explanatory or descriptive one.
The essay is often published with the foreword by his friend CP Snow, which takes up about the same length as the approximately 50 pages of the apology, which not only contains biographical details about Hardy, but also quotations from Hardy, often with the apology itself be associated.
Reception and criticism
Hardy's opinions were deeply from the academic ways of thinking from the universities of Cambridge and Oxford between the First and Second World War marked. In retrospect, some of Hardy's examples seem ill-chosen. He writes, for example: "Nobody has yet discovered a warlike purpose that is served by the theory of numbers or relativity, and it seems that nobody will do that for many years". Shortly thereafter, the application of the theory of relativity became part of the development of nuclear weapons , while number theory played a significant role in asymmetric cryptosystems . Even so, Hardy's most important examples of elegant mathematical discoveries that are of no use (proof of the infinite series of prime numbers or the irrationality of the square root of 2) are still valid. The applicability of a mathematical concept, however, is not the reason why he considered applied mathematics inferior to pure mathematics; the simplicity and sobriety inherent in applied mathematics led to its description. He assumes that, for example, the theorem of Rolle , despite its importance for analysis , cannot be compared with the mathematics developed by Leonhard Euler or Évariste Galois and by other pure mathematicians.
literature
- GH Hardy: A Mathematician's Apology . University Press, Cambridge 1940, ISBN 978-0-521-42706-7 , pp. 153 ( cambridge.org - 2004 reissue).
swell
- ↑ A passionate lament for creative powers that used to be and that will never come again , Snow in Hardy A mathematicians apology , Cambridge University Press 1994, p. 51
- ↑ Exposition, criticism and appreciation is work for second rate minds , Apology, p. 1
- ↑ It is a melancholy experience for a professional mathematician to find himself writing about mathematics . With these words the apology begins
- ↑ Jonathan Borwein: Commentary on the Apology ( Memento of the original from November 15, 2006 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. ( PostScript )
Web links
- The full text of A Mathematician's Apology - (PDF; 179 kB), public domain in Canada , courtesy of the University of Alberta Mathematical Science Society.