The History of Numbers

Introduction• Numbers serve two purposes

– Tools for Counting and Measuring– Attempt to Understand the Unexplainable

• Natural versus Learned Counting– Develop System & Method of Manipulation

– Linguistics to Communicate the System

Introduction• Civilizations each developed their own system, each contributing to today’s understanding of numbers

Babylonian Numbers

• Some of the Earliest Devices to Record Calculations– Clay Tablets in Iran of Base 10– Clay Tablets in Iraq of Base 60

• Both Counting Systems are Still Present in Society Today

Egyptian Numbers

• Number System is not well evidenced, but their contribution is undeniable

• The Temple of Wasat was the World’s first University– Educated 80,000 students at its peak

– Students included: ???

Egyptian Numbers

• Students included: Plato, Aristotle, Socrates, Euclid, Pythagoras, Hypocrates, Archimides, Euripides

Egyptian Numbers• Left Little Written Evidence of Mathematics

• Rhind Papyrus (1650 BCE) – Scroll 20’ x 1’ with 87 problems

Greek Numbers• Which is more basic: Arithmetic or Geometry?– Discrete or Continuous Universe

• Reality is Mathematical in Nature• Irrational Numbers Presented a Philosophical Problem for the Greeks

• Thinking Based on Words and Abstract Diagrams

Greek Numbers• By 500 BCE, they had a system based on the decimal and comprised of the 27 letters of their alphabet– First nine letters represented the digits 1-9

– Second nine represented the tens

Greek Numbers– The last nine represented the hundreds

– Special sign for numbers higher than 900

– There was no zero– Numbers were nonpositional

Roman Numbers• Roman numerals spread throughout Western Europe– Started with stick numbers (I, II, III, IIII)

– Added six letter symbols (V, X, L, C, D, M)– Addition & Subtraction were simple, but Multiplication & Division proved Complicated

– CCKCVI + DCL + MLXXX = ?

Roman Numbers

• The Abacus existed to provide place value– Work vanished as it was performed, leaving no record of the process

– No way to check results other than to redo the calculation

Arabic Numbers• In 830, Caliph al’Mamun founded the House of Wisdom in Baghdad– Advancement during European Dark Ages

– Muslim world was reading translated works of the great Greek mathematicians

Arabic Numbers• Arabic numerals were promoted by Fibonacci, but met opposition in Europe

• System had place value and zero

Mayan Numbers

• Employed a place value system with a base twenty counting system– They used a dot to represent 1 and a horizontal line for 5

– Larger numbers were represented by stacking symbols in columns

– Had a zero