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Mathematics in Historical Context

Mathematics in Historical Context

Jeff Suzuki
Series: Spectrum
Copyright Date: 2009
Edition: 1
Pages: 420
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  • Book Info
    Mathematics in Historical Context
    Book Description:

    Mathematics in Historical Context describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected by the outside world, and at the same time how the outside world was affected by mathematics and mathematicians. Part biography, part mathematics, and part history, this book provides the interested layperson the background to understand mathematics and the history of mathematics, and is suitable for supplemental reading in any history of mathematics course.

    eISBN: 978-1-61444-502-9
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Introduction
    (pp. vii-viii)

    This book emerged from a discussion I had with Don Albers in the Spring of 2002, when he suggested the idea of a book that would describe the world of the great mathematicians: “What would Newton see, if he looked out his window?” I really liked the idea, and planned to pick out a dozen or so mathematicians and write a hundred or so pages of history discussing how mathematics, society, and mathematicians interacted with one another. Before I knew it, I had written six hundred pages. I’ve cut those down to the present text, which is part mathematics, part...

  3. Table of Contents
    (pp. ix-x)
  4. 1 The Ancient World
    (pp. 1-14)

    When anthropologists speak of a group’s culture, they mean the sum of all the human activity of the group: how they talk, think, eat, play, and do mathematics. Every culture in the world creates some sort of mathematics, though it may be on a very basic level. The most ancient evidence of mathematical activity comes from a wolf’s bone on which fifty-five notches are carved, grouped in sets of five. The bone was found in the Czech Republic and is about 35,000 years old. A similar artifact was found at Ishango, on the shores of Lake Edward in Zaire. The...

  5. 2 The Classical World
    (pp. 15-54)

    Greece is a mountainous land of limited fertility, so settlements tended to cluster in the narrow valleys and on the various peninsulas that jut out into the Mediterranean. The relative isolation of the settlements encouraged them to form independent city-states. Like Sumeria, the individual Greek city-states were no match for a united conqueror, so by the time of A’h-mosè, mainland Greece was part of the Minoan Empire, centered on the island of Crete. The Minoan royal palace at Knossos was an impressive structure. Spread over six acres of land, it contained hundreds of rooms—and flush plumbing. Around 1500 b.c.,...

  6. 3 China and India
    (pp. 55-82)

    The easternmost of the great river civilizations of ancient times grew up along the banks of the Huang Ho (Yellow River) in China. Like the Nile, the Yellow River is rich in fertilizing silt (hence its name). Like the Tigris and Euphrates rivers, the Yellow River gives rise to disastrous floods, and as a result has received another name: China’s sorrow. According to tradition the Emperor Yao employed the engineer Kung Kung to build dikes along the Yellow River to control flooding. Unfortunately the dams merely collected water until they burst, causing even more severe flooding. One tale tells of...

  7. 4 The Islamic World
    (pp. 83-118)

    Before the seventh century, the Arabian peninsula was populated by nomadic Bedouin tribes who worshipped spirits they believed present in objects such as rocks, animals, and plants. In Bedouin mythology Allah was the supreme ruler of the universe, but there were others, such as Hubal the Moon God. But in 610 a merchant named Muhammad had a revelation: there is no God but Allah. In Arabic this is the sonorous refrain, “la ilaha illa Allah.” The denial of the very existence of other gods was made one of the five pillars of a new religion, soon known asIslam(“submission,”...

  8. 5 The Middle Ages
    (pp. 119-156)

    In 911, Charles the Simple ceded a section of coastal France to the Viking chieftain Rollo in exchange for a promise to convert to Christianity and to withdraw his warriors from Paris. Within a century the land of the Northmen (Nortmanni) became the well-administered, highly centralized state of Normandy.

    The Normans followed the rule of primogeniture, whereby the eldest son inherits all the lands of his father. Thus only one of the twelve sons of Tancred of Hauteville would inherit the family lands in western Normandy; the rest had to find their own fortunes. Luckily for them, southern Italy was...

  9. 6 Renaissance and Reformation
    (pp. 157-184)

    Europe slowly recovered from the plague. In part this was due to the fact that most of the susceptible population died in the first few years of the plague, but in part it was due to drastic measures taken by cities to prevent the plague from entering. In Italy, divided into a number of independent states, the port cities instituted the practice of interning a vessel’s cargo and crew for a period of thirty days before they were allowed to mingle with the general population: the original quarantine (fromquarantina, “forty” in Italian).¹

    The plague had two important effects. Since...

  10. 7 Early Modern Europe
    (pp. 185-230)

    In 1533, Francis I’s son Henry married the fourteen-year-old Catherine de’Medici, the granddaughter of Lorenzo the Magnificent. Catherine introduced gloves from Italian fashion to the French court, as well as Italianesque palaces (she herself designed the Tuileries, in Paris), comedy troups known ascomédie Italienneand later as the commedia dell’arte; dance troupes; and haute cuisine. Catherine also popularized a new habit at the French court. She suffered from migraines, so in 1550, the French ambassador to Portugal sent her a local remedy: powdered tobacco. The ambassador’s name was Jean Nicot.

    The most famous person associated with Catherine’s court was...

  11. 8 The Eighteenth Century
    (pp. 231-276)

    Neither William nor Anne (Mary’s sister, and William’s successor) produced an heir to the throne, so on June 12, 1701, Parliament passed the Act of Settlement which expressly stated that the crown of England would pass to Sophia of Hanover, the granddaughter of James I (and daughter of Frederick V the “Winter King”), or any Protestant children she might have, andnotto ex-king James or his children. Thus on William’s death in 1702, Anne became Queen of England and Scotland (Mary predeceased her husband).

    Anne knighted Newton in 1705 (the first scientist to be honored for his scientific work),...

  12. 9 The Nineteenth Century
    (pp. 277-310)

    In the aftermath of the Napoleonic Wars, the delegates at the Congress of Vienna sought to establish the balance of power as the key theme in European politics. The delegates joined small nations together to form larger, and theoretically more powerful, states. Belgium and the Netherlands, different in religion, language, and culture, became Kingdom of the Netherlands; the German states, different in religion and political orientation, were welded together into the German Confederation; and Sweden’s claim to Norway was recognized. It is perhaps no coincidence that Mary Shelley’sFrankenstein(1818), the story of a man who created a monster by...

  13. 10 The United States
    (pp. 311-336)

    In 1757, during the Seven Years’ War, French forces captured Hanover. Rather than sending more troops to the continent to retake Hanover, William Pitt the Elder proposed an alternative strategy of attacking French colonial interests overseas: in effect, turning the periodic skirmishes between the British and French in the contested Ohio River Valley into a major war, now known as the French and Indian War. The British captured Fort Duquesne in 1758, renaming it Pittsburgh, and by 1760, all of French Canada was in British hands. By the terms of the Treaty of Paris (1763), Britain received all of French...

  14. 11 The Modern World
    (pp. 337-384)

    Between 1830 and 1870, total enrollment in German universities remained steady at around twelve to thirteen thousand, but after unification the student population grew dramatically, nearly tripling by 1900. Many of the new students came from non-aristocratic backgrounds. Dueling clubs became very popular, as the right to carry a sword was traditionally reserved for the aristocracy. A dueling scar identified the bearer as sympathetic to (and deserving of sympathy from) the professionals and military officers who ran Germany.

    The dueling societies at the University of Heidelberg are legendary, and in 1885 a student at the Massachusetts Institute of Technology wrote...

  15. Epilog
    (pp. 385-386)

    In a very real sense, the history of the world prior to the world wars could be treated as a collection of individual regional histories: the history of Asia, the history of the Americas, the history of Europe, and so on. Occasionally one region might influence another: the Mongol invasion of Europe; the scientific accomplishments of the Islamic states; European imperialism in the Far East. But the effects were either brief (the Mongol Empire virtually vanished within a generation), limited (European colonies in China were mainly limited to the coastal regions), or episodic (Islamic mathematics played a formative role in...

  16. Bibliography
    (pp. 387-394)
  17. Figure Citations
    (pp. 395-396)
  18. Index
    (pp. 397-408)
  19. About the Author
    (pp. 409-409)