Day 1, Mat305/594, History of Mathematics:
Welcome and First Thoughts

Next time: discuss section 1.2

• Welcome!
  • Announcements
    • Thanks for signing up!
    • Sehnert Banquet and Lecture, October 12th (Monday evening, 6:15). This year we will have Frank Morgan ("Mr. Bubbles!").

• Before we get started, let's get acquainted. Use the 4x6 cards and let us know the following:
  1. Name
  2. Where are you from?
  3. Working? If so, where, and how many hours?
  4. Year (Sophomore, etc.)
  5. Major
  6. Why are you taking the History of Mathematics?
  7. Something special about yourself.

• Syllabus

• Approximate schedule.

• About the text, and author:
  • This is one of the standard academic treatises on Math History.
  • Burton has written an admirable text on Number Theory (which you may have used).
  • In addition to our textbook, I'll use materials from other textbooks, such as the on-line Math History text, Lectures on the History of Mathematics, by G. Donald Allen ( Texas A&M University). These may be accessed at the website www.math.tamu.edu/~dallen/masters/ (here's a local copy).

• For next time: sign your classroom agreement.

• Overview of the material of the course

  My plan is to cover (most of) the following chapters (you will be doing a lot of reading!):

  • Chapter 1: Early Number Systems and Symbols
  • Chapter 2: Mathematics in Early Civilizations
  • Chapter 3: The Beginnings of Greek Mathematics
  • Chapter 4: The Alexandrian School: Euclid
  • Chapter 5: The Twilight of Greek Mathematics: Diophantus
  • Chapter 6: The First Awakening: Fibonacci
  • Chapter 7: The Renaissance of Mathematics: Cardan and Tartaglia
  • Chapter 8: The Mechanical World: Descartes and Newton
  This will get us up to the time of Descartes, bumping up against the development of calculus (the most essential of modern mathematics). Some homework problems will make reference to modern techniques, and I also plan to have you investigate modern history through your papers and commercials, so modern mathematics will not be ignored.

• For next time:
  • Read Sections 1.1 and 1.2, with your worksheet and blank world map in hand. The map is two sided, because you're reading two sections.
  • Visit the Course homepage
  • Begin Homework, pp. 18--, #1-7

• Commercial: Srinivasa Aiyangar Ramanujan (1887 - 1920) and his encounter with G. H. Hardy

  (Note: your commercial will end with you giving me a two page "report" on the mathematician or idea, including a reference or two.)

  Suggestions for other commercials:

  • Florence Nightingale
  • Emmy Amalie Noether
  • Evariste Galois
  • Paul Erdos
  • Galileo Galilei
  • Andrew Wiles and Fermat's last theorem
  • Googolplex
  • The Abacus
  • Johann Carl Friedrich Gauss
  • Sir Isaac Newton
  • Leonhard Euler
  • Max Abraham
  • Gertrude Blanch
  • Joseph-Louis Lagrange
  • Sophie Germain
  • Bertrand Arthur William Russell
  • Benoit Mandelbrot
  • Maurits Cornelius Escher
  • Mary Fairfax Greig Somerville
  • Maria Gaetana Agnesi
  • Leonardo da Vinci
  Who will bravely get one of their commercials out of the way next week? Will anyone bravely get one out of the way next time?

• Some thoughts, as we begin:

  • My word of the semester: iteration

  • Why should we study the history of mathematics?

  • Learning Objectives

  • Introductory quote from our textbook:

    All these were honoured in their generations, and were the glory of their times.
    There be of them, that have left a name behind them, that their praises might be reported.
    And some there be, which have no memorial; who are perished, as though they had never been; and are become as though they had never been born; and their children after them.
    Ecclesiasticus 44:7-9

  • Lighthearted: where do mathematical ideas come from? (start at minute 2:20) -- but there is something to it....
    • What dictates how and what mathematics is undertaken?

  • Why did I bring a globe to class?

  • Why am I going to grade your writing skills in your paper?

  • Of what relevance is this quote: 'Those who cannot remember the past are condemned to repeat it.' (Who said it?)

  • Of what relevance is this quote: "History is written by the victors." (Attributed to Winston Churchill).
    • How will the victors write the history of Mathematics?
    • What else dictates how and what history is recorded?

  • From E. T. Bell, The Queen of the Sciences: "...in mathematics the man who is ignorant of what Pythagoras said in Croton in 500 B.C. about the square on the longest side of a right angled triangle, or who forgets what someone in Czecho Slovakia proved last week about inequalities, is likely to be lost. The whole terrific mass of well established mathematics, from the ancient Babylonians to the modern Japanese, is as good today as it ever was."

  • An extended reading from Bell, from whom I learned my initial history of mathematics (e.g. Bell's Men of Mathematics -- oops, what about the women?)

  • In section 1.1 you'll encounter an ancient bone into which tallies have been carved (the Ishango Bone, from Central Africa).
    Here's another ancient bone: Ancient flutes from 35,000 to 40,000 years ago.
    • What mathematics would have been required to construct such a flute?

  • Honey Bees can tell two from three: what do we conclude concerning the History of Mathematics?