1. History of Math
Numbers vs. Numerals

2. Number Definition 1: A symbol or word, or a group of either of these, showing how many or which one is a series. Definition 2: An idea corresponding to a quantity.
Numeral Definition: A figure, letter, or word, or a group of any of these, expressing a number What is the difference between these two words?
Definition

3. 6,000 BC African civilization in region between Uganda and Zaire
1957: A Belgion archeologist discovered a bone in a place called Ishango near the river Nile. The bone is over 8000 years old. Notching represented quantities

4. Ishango: By Lake Edward

5. Oldest Table of Prime Numbers
Microscopic examination showed 6 month lunar calendar represented.

6. 1) What is the sum of each row. 2) What is the pattern in row (a)
1) What is the sum of each row? 2) What is the pattern in row (a)? 3) What do you notice is true about all of the numbers in row (b)? 4) What is the pattern for the numbers in row (c)?

7. 3000 B.C.
Quipu: Pre- Incan Civilization in Caral

8. Pre-Incan and Incan Empire
The Quipu is a system of knotted cords thought to represent quantities

9. Since most of the Incas were wiped out and the Spanish thought the Quipu was idolatrous, they enthusiastically exterminated knowledge of how to use the Quipu

10. Written Numerals Ancient civilizations tried to model numbers
Tick marks and knots
Ancient Numerals
not efficient for “large” numbers
Led to new inventions for numerals
Written Numerals

11. Mesopotamia Writing started as early as 4000 BCE
Used Cuneiform as a form of writing to measure numbers.
Cuneiform scribes wrote with a triangular stylus that was plunged into wet clay forming different indentations depending on the angle of the plunge
The tablets typically did not show procedures, but recorded arithmetic results
Mesopotamia

12. Roman Numerals Radix Number System
This system allows a lower number symbol to modify the meaning of the symbol for a larger number.
A radix occurs when a new symbol is introduced and represents the set of next smaller symbols.
“radix” typically refers only to systems with a fixed radix called the base.
What is a type of Radix system?
Roman Numerals
Radix Number System

13. Measuring using numbers
The Chinese have the current earliest claim to measuring quantities using numbers
Ping-Ti Ho studied Yangshoa pottery(around 4500 BCE)which was used to make markings to measure pots, or volume.
This actually might be among the earliest examples of written numbers, because there were symbols similar to Roman numerals
Measuring using numbers

14. All civilizations needed a way to measure time…why?
Measuring Time

15. Resources An Introduction to the History of Mathematics by Howard Eves
Writing – Ancient History Encyclopedia (
Quipus Knots Index, Inca Empire (incas.homestead.com/quipu)
Quipu of Secrets: A different kind of string theory (
A History Of Numerals (
Ishango Bone (
Resources