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A Wealth of Numbers

A Wealth of Numbers: An Anthology of 500 Years of Popular Mathematics Writing

Edited by Benjamin Wardhaugh
Copyright Date: 2012
Pages: 392
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  • Book Info
    A Wealth of Numbers
    Book Description:

    Despite what we may sometimes imagine, popular mathematics writing didn't begin with Martin Gardner. In fact, it has a rich tradition stretching back hundreds of years. This entertaining and enlightening anthology--the first of its kind--gathers nearly one hundred fascinating selections from the past 500 years of popular math writing, bringing to life a little-known side of math history. Ranging from the late fifteenth to the late twentieth century, and drawing from books, newspapers, magazines, and websites,A Wealth of Numbersincludes recreational, classroom, and work mathematics; mathematical histories and biographies; accounts of higher mathematics; explanations of mathematical instruments; discussions of how math should be taught and learned; reflections on the place of math in the world; and math in fiction and humor.

    Featuring many tricks, games, problems, and puzzles, as well as much history and trivia, the selections include a sixteenth-century guide to making a horizontal sundial; "Newton for the Ladies" (1739); Leonhard Euler on the idea of velocity (1760); "Mathematical Toys" (1785); a poetic version of the rule of three (1792); "Lotteries and Mountebanks" (1801); Lewis Carroll on the game of logic (1887); "Maps and Mazes" (1892); "Einstein's Real Achievement" (1921); "Riddles in Mathematics" (1945); "New Math for Parents" (1966); and "PC Astronomy" (1997). Organized by thematic chapters, each selection is placed in context by a brief introduction.

    A unique window into the hidden history of popular mathematics,A Wealth of Numberswill provide many hours of fun and learning to anyone who loves popular mathematics and science.

    eISBN: 978-1-4008-4198-1
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-xii)
  3. Preface
    (pp. xiii-xviii)
  4. 1 “Sports and Pastimes, Done by Number”: Mathematical Tricks, Mathematical Games
    (pp. 1-31)

    You’ve probably played a mathematical game at one time or another. From the counting games we learn as children and the calculator tricks we play in the schoolyard to classics like Sprouts or Lewis Carroll’s Game of Logic, there’s a whole world of game playing to be had in the realm of numbers. Mathematicians used to be accused of doing magic (some still are), and while conjuring spirits or divining the future may be far from what most of us think of when we think of mathematics, there is a timeless innocent pleasure in the wool-over-the-eyes mathematical tricks of the...

  5. 2 “Much Necessary for All States of Men”: From Arithmetic to Algebra
    (pp. 32-61)

    Arithmetic never had a Euclid. To be sure, there were important systematic accounts of the subject from the earliest times; but none of them acquired anything like the status or the longevity of theElements(for one reason why not, see Charles Hutton’s account of the history of arithmetic in Chapter 7). So when the printing press arrived, the field was wide open for individual vernacular writers to dominate for a very long time. It was Robert Recorde (c. 1512–1558) who achieved that status as far as English mathematics writing was concerned, and we begin this chapter with him...

  6. 3 “A Goodly Struggle”: Problems, Puzzles, and Challenges
    (pp. 62-83)

    “Because it’s there” is a good reason for climbing a mountain—so they say—and it seems a good reason for doing a mathematical problem, too. Mathematicians involved in new research had set each other challenges and gone head to head in competitions since at least the sixteenth century, but competitive puzzling at an amateur level boomed early in the eighteenth century withThe Ladies’ Diary, the source of our first extract.

    TheDiary, likeThe Athenian Mercurywhich we will meet in Chapters 5 and 10, was one of the “new media” of its day, offering readers a chance...

  7. 4 “Drawyng, Measuring and Proporcion”: Geometry and Trigonometry
    (pp. 84-107)

    “Geometry teacheth the drawyng, Measuring and proporcion of figures,” wrote Robert Recorde. It also teaches logical thought, and for many years geometry was taught both as a worthwhile study for its own sake and also as a way to discipline the mind and make it fit for other studies.

    Unlike arithmetic, geometry did have a Euclid, and theElements, “the greatest [textbook] the world is privileged to possess” (see Thomas Heath in Chapter 7), proved all but irresistible as a model for generations of textbook writers. Straightforward translations of theElementsinto English number dozens; many and many were the...

  8. 5 Maps, Monsters, and Riddles: The Worlds of Mathematical Popularization
    (pp. 108-151)

    Popularizing mathematics is a game with two halves. The first half took place in the early eighteenth century, in a world amazed by the phenomenal success of Newtonian science and, perhaps, anxious about what mathematics now meant and did. Quite a lot of the popular mathematical writing of this period appeared in the specific context of explaining Newtonian science to the nonspecialist, and our extract from the lovelyNewton for the Ladiesillustrates both this and what would much later become a vitally important line in popular science writing: “it can be proved that . . . .” Trust me,...

  9. 6 “To Ease and Expedite the Work”: Mathematical Instruments and How to Use Them
    (pp. 152-175)

    No one wants to read excerpts from an old calculator manual. Yet instruments have been important throughout the history of mathematics, and a very important and prominent dimension of the mathematics writing of the past is writing about mathematical instruments of one kind or another: making them, using them, where to buy them or have them repaired. It would be a pity to miss out on this material, but of course it presents the obvious problem that quite a lot of it is simply incomprehensible unless you have the instrument in question in your hands.

    So this chapter is a...

  10. 7 “How Fine a Mind”: Mathematicians Past
    (pp. 176-215)

    Interest in mathematicians past began in the sixteenth and seventeenth centuries with the rediscovery, publication, and commentary on ancient mathematical texts, part of the more general Renaissance concern to rediscover and surpass ancient learning (and a process which continues to this day: “new” texts by Archimedes have been in the news in the last few years). This side of mathematical history writing is represented elsewhere in this book by the passage from Euclid in Chapter 4.

    Also on display in other chapters is guessing—or, to be kinder, speculation—about the origins of mathematical techniques. We’ve seen both Joseph Fenn...

  11. 8 “By Plain and Practical Rules”: Mathematics at Work
    (pp. 216-244)

    A great deal of writing about mathematics is about mathematics in use: applied mathematics, as the modern term has it. Naturally quite a lot of that material is aimed squarely at specialists—whether professionals or amateurs in the field concerned—and assumes a good deal of background knowledge about the subject to which mathematics is being applied. Much makes no sense without specific instruments or tables in hand (a tendency was for books to be tailored to the use of specific instruments and tables produced by the same author or a crony), and many deal in extreme detail with highly...

  12. 9 “The Speedier Expedition of Their Learning”: Thoughts on Teaching and Learning Mathematics
    (pp. 245-289)

    “Arithmetic is a very dull study to children, and if the rod and the slate hang side by side, it cannot fail to be a disagreeable one,” wrote Mrs. Lovechild in 1785. This chapter showcases a few of the many ways that mathematics teaching has been thought about and practiced over the years, and some of the ways different writers have tried to avoid making mathematics “dull and disagreeable.”

    We will see both examples of practice and more reflective discussions: Humfrey Baker’s list of the mathematical subjects he taught to the “servants and children” at his London school, or the...

  13. 10 “So Fundamentally Useful a Science”: Reflections on Mathematics and Its Place in the World
    (pp. 290-325)

    Galileo famously claimed that the book of nature is written in the language of mathematics, and both before and since his time mathematicians and philosophers have tried to work out the details, the limits, and the meaning of the applicability of mathematics. We have seen, in Chapter 8, mathematics at work in various contexts; in this chapter we see mathematics being used more publicly: in politics or large-scale astronomy, in early modern natural philosophy, and in modern physics. In parallel we see its ever more public role being reflected upon.

    One strand of those reflections is a particular flavor of...

  14. 11 The Mathematicians Who Never Were: Fiction and Humor
    (pp. 326-366)

    Does it signify? Full of terms that outsiders don’t understand, full of things that don’t exist in the real world (lines with no breadth, points with no size), full of apparent nonsense yet full of ambition to change the world: mathematics has long been a rich field for fiction, humour and satire. Fictional treatments of mathematics often focus on individual mathematicians, and these “mathematicians who never were” are much on display in this chapter. They include desert-island autodidacts, astronomers both admirable and absurd, and fantastic visions of the mathematicians of the distant past or of other worlds.

    This riot of...

  15. Index
    (pp. 367-370)