The Unique Style of A Mathematician's Apology
Quite recently, I read A Mathematician's Apology, an essay written in 1940 by the famous English mathematician, G.H. Hardy. The essay serves as sort of a "defense" for Hardy, with his concern being to explain to the regular layman why he spent his entire life doing mathematics and discuss the beauty and satisfaction that mathematics provides.
Hardy wrote this essay when he was 62, which was when his mathematical prowess was slowly dying down. Hardy uses this essay to explain why his branch of mathematics, number theory, is the most beautiful branch of mathematics as back then, it barely had any practical use and mathematicians who would practice number theory mostly did so for the aesthetics of it. Hardy believed that branches of mathematics whose findings could be applied to real life and had any practice use were ugly and dull He says that applied mathematics would give material satisfaction but in the long run, doing pure mathematics that only possesses mathematical beauty and no real application would make a mathematician happier. Carl Gauss, the mathematical prodigy, once said that mathematics is the queen of all sciences and number theory is the queen of mathematics. Hardy says that Gauss meant that number theory is the queen due to its beauty and elegance, not because it is the most useless and therefore deemed trivial by mathematicians. "If the theory of numbers could be employed for any practical and obviously honorable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good (and particularly, of course, in time of war); and both Gauss and less mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean." (Hardy, 33)
Part of Hardy's purpose for writing A Mathematician's Apology was to justify to the regular person and non mathematical community why he remained a pacifist through World War I. His point in this was to explain that his pursuit of mathematics was to find the pure beauty that it posseses, not to try and find the practical applications for it, which might have aided in destroying humanity. There are many occasions in the essay where Hardy's disdain for applied mathematicians comes through, and he makes it clear that he wants the future generation of mathematicians to know that true joy lies in discovering the beauty that mathematics possesses, even if it may not have any practical applications. A Mathematician's Apology sort of serves as a justification for Hardy's life's work; it's a way for him to express to the ordinary citizen why he devoted his entire life to a useless yet beautiful branch of mathematics.
I found the style of the essay to be very engaging and Hardy does not make it very mathematically technical, as his point is to reach a broader audience. This essay is definitely a must read for anyone who loves mathematics and finds enjoyment in thinking about the beauty that mathematical patterns possess, but really, anyone can read it and it will be sure to spark your interest in the aesthetics of mathematics. The essay does contain some proofs, but they are fairly easy to understand for anyone who has had a middle school level of education in mathematics, and the purpose of these proofs is to show the elegance that they possess. I would give this essay a 5/5.
Hardy wrote this essay when he was 62, which was when his mathematical prowess was slowly dying down. Hardy uses this essay to explain why his branch of mathematics, number theory, is the most beautiful branch of mathematics as back then, it barely had any practical use and mathematicians who would practice number theory mostly did so for the aesthetics of it. Hardy believed that branches of mathematics whose findings could be applied to real life and had any practice use were ugly and dull He says that applied mathematics would give material satisfaction but in the long run, doing pure mathematics that only possesses mathematical beauty and no real application would make a mathematician happier. Carl Gauss, the mathematical prodigy, once said that mathematics is the queen of all sciences and number theory is the queen of mathematics. Hardy says that Gauss meant that number theory is the queen due to its beauty and elegance, not because it is the most useless and therefore deemed trivial by mathematicians. "If the theory of numbers could be employed for any practical and obviously honorable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good (and particularly, of course, in time of war); and both Gauss and less mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean." (Hardy, 33)
Part of Hardy's purpose for writing A Mathematician's Apology was to justify to the regular person and non mathematical community why he remained a pacifist through World War I. His point in this was to explain that his pursuit of mathematics was to find the pure beauty that it posseses, not to try and find the practical applications for it, which might have aided in destroying humanity. There are many occasions in the essay where Hardy's disdain for applied mathematicians comes through, and he makes it clear that he wants the future generation of mathematicians to know that true joy lies in discovering the beauty that mathematics possesses, even if it may not have any practical applications. A Mathematician's Apology sort of serves as a justification for Hardy's life's work; it's a way for him to express to the ordinary citizen why he devoted his entire life to a useless yet beautiful branch of mathematics.
I found the style of the essay to be very engaging and Hardy does not make it very mathematically technical, as his point is to reach a broader audience. This essay is definitely a must read for anyone who loves mathematics and finds enjoyment in thinking about the beauty that mathematical patterns possess, but really, anyone can read it and it will be sure to spark your interest in the aesthetics of mathematics. The essay does contain some proofs, but they are fairly easy to understand for anyone who has had a middle school level of education in mathematics, and the purpose of these proofs is to show the elegance that they possess. I would give this essay a 5/5.
I found your post and analysis of the book fascinating. Often people when discussing math focus on "why is this applicable, how can this actually be used" whereas this is a completely different opinion. You nicely explained his opinion and love for the beauty of math, and helped me understand the book in a general sense. Nice post!
ReplyDeleteThis was an interesting blog post to read, because it is something that I would never read or pick out myself. I personally don't find math to be the most interesting to read about but your analysis of this book was intriguing. I liked how you included how this book could be read by more people than just those who know math terms, which let me know that maybe I could read it at some point without being completely lost. Very cool and different blog post - I really liked it!
ReplyDeleteGood job on this blog post. I found this interesting because I don't usually read these kind of books. I think it's cool how the author is trying to reach out to more people than ones just interested in math because the general population doesn't understand how there could be any beauty in math, and this could open up some peoples eyes to that. Overall, good post, and I might check this book out to maybe spark a new interest in me,
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