Early Mathematics and Number Systems

Study Notes

Early Mathematics and Number Systems

The term "mathematics" originates from the Greek word "mathemata," meaning "subject of instructions" or "to learn/study."
Mathematics emerged in classical Greece between 600 and 300 BC, defined as a science dealing with quantities, magnitudes, forms, and their relationships using numbers and symbols.

Tallying and Early Counting Methods

Tallying derives from the French verb "tailler," meaning "to cut," and involves matching items to be counted with easily manageable objects.
Early tallying used shells or stones; for instance, sheep could be counted by guiding them through a narrow passage and dropping a pebble for each.
Historical bone artifacts have been found with notches, indicating that early humans created tally systems, like the shinbone of a wolf with 55 notches.

Ishango Bones

Discovered in 1960, the Ishango bones are estimated to be 6,000 to 9,000 years old and show early tallying methods.
These bones, with incised markings, are believed to represent hunting tallies or kills.

Knot-Based Number Systems

In the New World, the Quipu system used knotted cords for numerical representation, with different knots indicating different values (e.g., figure-eight knot = 1).
Quipus included a main cord with attached cords of varying lengths and colors, representing numerical values.

Egyptian Number Recording

Egyptians had a developed number system as early as 3500 BC, capable of indefinite counting through the addition of new symbols.
Their writing system utilized hieroglyphs, where each character represented a concrete object, recognizable in some contexts.

Hieratic Script

Egyptians invented papyrus from the papyrus plant, used for writing with a brush-like pen made of ink from colored earth mixed with gum and water.
Hieratic writing, a cursive version of hieroglyphics, presented symbols in a free-running hand style, distinct from the original pictorial form.

Herodotus: Historical Context

Herodotus (circa 485-430 BC), born in Halicarnassus, was exiled and traveled extensively as a merchant and historian, documenting his findings.
His journeys included sailing up the Black Sea and exploring Egypt, where he ascended the Nile and observed the pyramids.

Greek Alphabetic Numeral System

Around the 5th century BC, the Greek Ionia developed a ciphered numerical system with a broader array of symbols needing memorization.
The Greek alphabetic system enabled sophisticated mathematical expression and record-keeping.

Description

Explore the roots of mathematics, from its origins in ancient Greece to early tallying methods used by humans. Learn about the significance of the Ishango bones and their contribution to our understanding of numerical systems. This quiz highlights key concepts and early practices that shaped mathematical development.