Essay: 'Mathematicians Apology' – Dr. Godfrey Harold

The author of ‘Mathematicians Apology’ is Dr. Godfrey Harold, and it had published first time at 1940 in England. Prof. Harold is memoir of world renowned mathematicians, and this book was written while he was in failing health, and throughout this essay but there is no
Doubt at all about the feelings of men of science, and I share them fully. If then I find myself writing, not mathematics, but ‘about’ mathematics’, and I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job’. He discards the language he would use in his research/academic paper instead adopts a succinct and simple writing style aimed to non-physical science major general author. The book ‘Mathematicians Apology is a lasting testament to Hardy’s passion for intellectual pursuit. He links mathematics to art and beauty, and explains math in way a critic explains art. On chapter 2, ‘propose to put forward an apology for mathematics”.profitable and praiseworthy. He introduces the fundamental question that he proposed, about mathematical study, justification of a mathematician’s life, and philosophy of mathematicians. On chapter 3, Hardy discuss about career, he dedicated it as justification of existence and activities, he also status it can be separated two different parts, first. Weather the word which he does worth doing, second, why he does choose that careers. He could not sufficiently answer first part of questions, and he only focused on second part of questions. He proposed his theory as following: ‘if they are honest, will usually take one or other two forms; and the second form is a merely a humbler variation of the first, which is the only answer we need consider seriously’. Which means that most people choose career path because ‘It is the one and only things they can do at all well: He brought out some fields of career example such as lawyer, stockbroker, and professional cricketer. In my personal interpretation, these field of career is required some kind of talent and passions like lawyer, lawyer is required fluent tongue, proficient of debating and manipulate which is talent, and interested in legal subtleties and, passions of argument and debating, these kind of thins are almost always be dedicated by limitation of the natural abilities, but these techniques are not able to applied for poet, physicist and mathematician. He states, the field of career and professional ties in mathematicians are one of the most specialized talents and it is undeniable inherent gift which is a particularly specialized subject, and mathematicians themselves are not noted for their versatility On following chapter (chapter 4) he discussed several famous mathematicians who attempted new careers late in life and were largely failure. On his article, he questioned about the age of mathematician, and he assumed that mathematicians are not allowed to forget the knowledge in mathematics. The mathematics is considered are and science that is reason why most colleges’ math departments are part of college of art & science, or college of natural science. The ages in mathematicians are distinguishable, it is young man’s game. His status that average age of election to the Royal Society is lowest in mathematics. He point out several famous mathematicians whom gave us huge impacts. As example, Newton who invented law of gravitation and fluxions, gave up mathematics at age of 50, and lose his enthusiasm, his heady of mathematician’s career was mid 20 at time he invented these theory, and he dedicated it as prime of his age for inventions. After their retirement, they were looking for new careers, but their career was no successful such as, Laplace whom invented most fundamental theorem in differential equation and also used in electrical engineering (we need to thank you to prof. Laplace for his invention, because of him we are using highly sufficient smartphone and compute), his political career was highly discreditable, he is hardly a fair instance since he was dishonest rather than incompetent, and he abandoned mathematics which is just gave up he mathematics. On chapter, he answered question that he proposed at prior chapter (chapter 3), second part of question on career: ‘why he does choose that careers’ why he choose career is mathematicians and what he and other mathematicians means by mathematics. He outlined for apology for mathematics throughout his inaugural lecture at Oxford University in 1920. His one page lecture note gave very clear answer, he poised that mathematics is choose for following three reasons, first: it is essentially a “harmless” profession ‘the study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation’ . Let focus word ‘mathematics unprofitable: it is kind of hard to give direct answer yes or no, Om’. let ask same question on other point of view, does mathematics useful? Yes definitely mathematics is useful, and it is fundamental knowledge of other science such as chemistry and physiology. Second, the study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation. And: third, there is a “permanence” of mathematics that is “beyond the powers of the vast majority of men. These things are what Hardy adds what he believes are the three prime motivation that impel men to choose professions: intellectual curiosity, professional pride, and ambition for reputation and the rewards it brings. He concludes with a dream that mathematician and philosopher. He brought out ancient civilizations that are long forgotten save for their mathematical discoveries to support above theory. Bertrand Russell once related that expressed Russell’s deep-seated fear that he would one day be forgotten by future generations. ‘Academic career is one sought
Mainly by cautious and unambitious persons who care primarily for comfort and security’ this quote is also related to age of mathematics. In his essay, he mentioned professors and job security discourage passion of mathematics. Yes, it is definitely make sense, in most country adopted U.S college system, Assistance Professor lowest rank of professor who does not have job security, and also they are young, therefore they put their effort in research to award tenure, but after their tenure they have job security, and it discourage passion on mathematical research. On chapter 10, Hardy posits that mathematics has an aesthetic quality like that of art or poetry’a position for which he and this book are best remembered. He focused on world ‘idea’ he linked two different field of career between Mathematicians and painter or poet. ‘If his patterns are more permanent than theirs, it is because they are made with ideas. A painter makes patterns with shapes and colors, a poet with words. A painting may embody and ‘idea’, but the idea is usually commonplace and unimportant’. He takes a swipe at one of his contemporaries, mathematician Lancelot Hogben, who was well-known for his opposition to Hardy’s theories. Hardy uses the example of chess to refute Hogben. Because chess is revered by the masses and is an exercise in pure mathematics, though admittedly of a “lowly kind,” when one appreciates the beauty of a particular chess move, one is in essence appreciating its mathematical beauty but since the best mathematics also demands “seriousness,” or “importance,” and since no chess player or problem “has ever affected the general development of scientific thought,” chess is “trivial” compared to pure mathematics. On chapter 12, Hardy uses the examples of proofs by Euclid and Pythagoras to illustrate the beauty of mathematics. The following theorem explains why they are significant in spite of the fact that they are not practical. And Hardy continues to refine his concept of mathematical beauty by further defining the idea of “seriousness.” To do this, he introduces the concepts of “generality” and “depth. (please refer attached paper)

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