Early Mathematics and Number Systems

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.