The Oxford Handbook of the History of Mathematics (Oxford Handbooks) 1st Edition by Eleanor Robson (PDF)

Description

This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textualsources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking.Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood.The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: ‘Geographies and Cultures’, ‘Peoples and Practices’, and ‘Interactions and Interpretations’. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East,India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The Oxford Handbook of The History of Mathematics”We hope this book will not be what you expect” is the first sentence of this book. Indeed, it is not. It is not a “Handbook of the History of Mathematics”.The book consists of 36 articles on aspects of the history of mathematics more suited to academic journals as each assumes a prior knowledge of the subject. Topics range from mathematics as “the secret weapon of cultural imperialism”; to “the extent to which developments [of mathematics around 1900] can be regarded as `modernism’ similar to the rise in modernism … in [Pablo Picasso] painting, music, and literature”; to Rolle’s theorem; to Islamic art; and mathematics in the Third Reich. One article does reproduce 14 welcome frontispieces of classical mathematical tomes and the article on the Nicolas Bourbaki (a pseudonym for a 1930’s group of young French mathematicians) is simpler and more what the reader expects from the title and blurb on the back cover.The introduction tells us that “To limit the history of mathematics to the history of mathematicians is to lose much of the subject’s richness”; and “… the ways in which people have chosen to express themselves – whether in words, numerals, or symbols, whether in learned languages or vernaculars – are as historically meaningful as the mathematical content itself”; and so on. There you go – not what you expect!

⭐First of all: go to the Oxford Press to read: “Oxford Handbooks – the world’s most trusted source for scholarly research reviews” This book is not for populsr consumtin. Handbooks seldom are — back in college I used the CRC Handbook. Recently, I had to review a handbook of oil field drilling. Try and imagine that.Handbooks are for professional use.Where I’m coming from — I’m an associate professor of mathematics at a very large research university. When I go into the math library, I see row after row of popular ‘history of math’ books. I’d estimate something like fifty to seventy. Many of them repeat the same stories about math, based on research done in the lare eighteen to early nineteen hundreds.It’s no no longer the nineteenth century. This is the new research that will define the history of math for the next fifty years. This is not to say the other reviewers are ‘wrong’ — unless you are a researcher, or understand research based books, you might well be bored. I did, however, point out there are fifty or sixty alternatives.For me, the articles gave me new perspectives, challenged me to rethink what I thought I knew,I like it a great deal, and I’ve enjoyed reading many of the articles.

⭐This so-called handbook embodies a transformation of the field of history of mathematics that has taken place within the last generation or two of historians. To wit, historians of mathematics have abandoned all traditional goals of the field and alienated their traditional audience, and they imagine themselves superior for it.Suppose for example someone turned to this book looking for information on the history of the calculus. After all, hundreds of thousands of people study calculus every year, so it stands to reason that a bit of historical background about it would be a useful inclusion in a “Handbook of the History of Mathematics.” Alas, the reader will be disappointed. Despite the book’s detailed 28-page index—which includes for example 40 entries for “weaving and mathematics”—there is not a single entry on the calculus. Perhaps the reader knows that Leibniz was one of the creators of the calculus. He might be relieved to find that Leibniz at least exists in the index, with three entries, as many as Pablo Picasso (sic). These three entries concern his letters to Peter I, his priority dispute with Newton, and Rolle’s posturing against his calculus in the Paris Academy. In other words: patronage, power struggles, and rhetoric—fashionable topics that fascinate the modern historian of mathematics far more than that antiquated substrate that is mathematics itself.A reasonable reaction would be to conclude that this is not really a “handbook” at all as much as an excuse for historians to ramble on any esoteric topic of their fancy under the imprimatur of Oxford University Press. But that would be to underestimate the magnitude of the recent revolution in historiography. For it is not the notion of handbook that has been redefined, but the notion of history of mathematics. Gone are the days when the history of mathematics concerned itself with the evolution of the greatest accomplishments of the human mind. And gone with them are virtually every reason anyone ever had to take an interest in the subject in the first place, other than to further their own academic careers. Idiosyncraticism is now the order of the day, as Unguru once noted with pride:”History is primarily, essentially interested in the event qua particular event … History is not (or is primarily not) striving to bunch events together, to crowd them under the same heading by draining them of their individualities. … The domain of history, then, is the idiosyncratic.”This peculiar definition of history is an article of faith for the modern breed of historians. Strangely enough, however, they do not realise that they have radically redefined the field, let alone that in doing so they have emptied it of purpose in the eyes of many. The evolution of mathematical thought is of obvious interest to mathematicians, teachers, philosophers and curious people in general. Fewer are likely to be impressed by studies of “the event qua particular event.”If one is interested in the evolution of thought it obviously makes sense to adopt the opposite of Unguru’s view of what history is, namely to strive to bring out and explain the essential in history, as opposed to the idiosyncratic. When Newton brought out the underlying laws of mechanical phenomena, he certainly did not do so by studying “the event qua particular event.” On the contrary, a falling apple must be conceived as an abstract point mass before any meaningful scientific investigation can begin. It would make no sense to criticise Newtonian mechanics for failing to take into account whether the apple is red or green, sweet or sour. Yet when it comes to history of mathematics modern historians pride themselves on precisely such an attitude. Thus we read in the editors’ introduction:”To limit the history of mathematics to the history of mathematicians is to lose much of the subject’s richness. Creators and users of mathematics have included cloth weavers, accountants, instrument makers, princes, astrologers, musicians, missionaries, schoolchildren, teachers, theologians, surveyors, builders, and artists.” (p. 2) “Further, the ways in which people have chosen to express themselves—whether with words, numerals, or symbols, whether in learned languages or vernaculars—are as historically meaningful as the mathematical content itself.” (p. 3)The implicit adoption of the idiosyncraticist definition of history is evident, and it is only by recognising it that we can see that this is a handbook after all, albeit not of history of mathematics in any conventional sense. In this new kind of history all that matters is to “paint a complex and rich picture” (p. 311) “sensitive to its cultural context” (p. 798). Tracing currents of mathematical thought has ceased to be history and is therefore understandably absent from a handbook of it.But the modern historians are not satisfied with having appropriated the field and emptied it of purpose. They are also keen to tout their own superiority for doing so. Thus for example Imhausen’s chapter is devoted to attacking “an outmoded historiography” (p. 785) and its resulting “myths” regarding Egyptian mathematics. The first “myth” is that of the “Egyptian pi.” Here she scolds scholars like Cantor and Neugebauer for rephrasing an Egyptian method of computing areas of circles in modern terms as corresponding to a certain value of pi. Like her other “myths,” this is plainly no myth at all. It is an accurate description, and one that makes sense given the traditional and commonsensical goals of historical scholarship. But of course it is madness if one redefines the meaning of history in accordance with the idiosyncraticist manifesto. Then, sure enough,”It is remarkable that secondary literature is more concerned with the fact that Egyptian mathematics arrived at such a good approximation for pi than with the actually rather striking observation that Egyptian mathematics used a procedure that did not involve pi but resulted in a comparatively accurate result.” (p. 789)”Remarkable” indeed, if one cares more about the colour of the apple than the law of its fall; but otherwise not. Modern historians moralising about “outmoded historiography” are so impressed by their own supposed superiority that they fail to see that it is based on a redefinition of the field rather than intrinsic merit.

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