Day 2, Mat305/594, History of Mathematics

Last time: Welcome, and first thoughts

Next time: discuss section 1.3

Today:

• Announcements
  • Math Club flier
  • Sehnert Banquet and Lecture, October 12th (Monday evening, 6:15). This year we will have Frank Morgan ("Mr. Bubbles!").
  • Can I get your agreements?

• So: what do you think of the book?

• Into the mire and the muck! Several things today:
  • Worksheet for section 1.3 (for next time)
  • Unresolved issues from last time
  • Lessons from section 1.1
  • Lessons and problems from section 1.2

• Some unresolved issues from last time, before we begin:
  • 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?

• Lessons from section 1.1
  • Questions from the 1.1-1.2 worksheet?

  • What are the geographic elements you identified in section 1.1?

  • Mathematical Elements?

• Lessons and problems from section 1.2
  • What are the geographic elements you identified in section 1.2?

  • Mathematical Elements?

• Problems, pp 14--, #1-7: any we should look at?

• Americas:
  • Amerindian Civilizations
  • Inca Road System
  • Amazon tributaries
• Old world:
  • Hammurabi's Babylonia, showing the Babylonian territory upon his ascension in 1792 BC and upon his death in 1750 BC
  • Persian Empire at the time of Darius (approx 500 BC).
  • A site with some math history and maps

• Tallies
  • Tally tokens
  • Tally sticks
  • Tally cords
• Mayan vigesimal system
  • first symbol for zero
  • numerals of the priestly class, and of the common people
  • minor variation: not pure powers of 20

• "The habitable world according to Herodotus"
• Halicarnassus, home of Herodotus
• Samos Island (click on the dot next to the lat/long for Samos)
• Athens
• Dnieper River
• Caucasus Mountains
• The Nile(s) (unified by Menes, about 3100 BC. 31 dynasties until Cleopatra "encounter with the asp")
• Ancient Egypt
• Ionia

• Egypt's decimal heiroglyphic numeral grouping system
• subtraction and addition operations by 1650 BC (Rhind papyrus)
• Egyption Hieratic numeration. "cipherization": a "decisive step in the development of numeration" (p. 16)
• Greek alphabetic numeral system, based on an augmented greek alphabet (the cipher)
• multiplication essentially a distributive ("grouped") operation
• alphabetic notation led to "gematria" -- e.g. 666, the number of the beast; "AMEN"=99; or Pompeii graffiti "I love her whose number is 545." (What was her name in Ionic greek?)