Now Playing: Faerie Window Source: Inventions and Discoveries, 1993 by Valerie-Anne Estaing

Numeration (3000 B.C.) Numbers were first written in the third millenium B.C., as is attested to by the clay tablets discovered in Susa and Uruk (currently Warka and Iraq). The Babylonian system of numeration is on a base of 60 Our time divisions are a vestige of this. There was no zero; missing units were simply indicated by a space.

Irrational Numbers (c. 6th Century B.C.) Pythagoras demonstrated the impossibility of writing the number (root 2) as a fraction, and hence revealed the existance of irrational numbers.

Pythagoras' Theorem (6th century B.C.) Pythagoras, the Greek philosopher and mathematician established a relationship between relationship between the lengths of the sides of a right angle triangle: that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This relationship was known by surveyors but Pythagoras was the first to demonstrate it.

Zero (c. 4th Century B.C.) Babylonian numeration was perfectd in the 4th century B.C. by the appearance of zero in mathematical texts. The zero was placed at the beginning or within a number, but never at the end. The word zero comes from sunya meaning nothing.

The Number (Pi) (3rd Century B.C.) By using polygons of 96 sides inscribed and excribed to the circle, Archimedes demonstarated that the number pi was located between (3+ 10/71) and (3+ 10/70). Thus, when Ptolemy adopted the value of 3.1416 for pi he noted, to justify it, that it was nearly the mean of the two Archemedian boundaries.

Trigonometry (3rd-2nd Century B.C.) Trigonometry developed as a technique annexed to astronomy. The first to apply the principles of trigonometry were astronomers Aristarchus of Samos, Hipparchus of Nicea, and Ptolemy. The Arabs eventually developed trigonometry as a seperate science and Al Khwarizmi established the first sine table and Habasch al Hasib established the first tangent table. It wasn't until the 16th century that trigonometry became integrated with algebraic techniques.

Modern Numeration (5th Century A.D.) Around the 5th century A.D., arithmetic using ten figures from 0 to 9 appeared as we know it today in India. However, it wasn't until 1202 when the Arabic system of numbers gained popularity in Europe.

Algebraic Symbols (15th - 17th Century A.D.) It was not until the 15th century in which the English, Germans and French introduces symbols instead of written words to signify algebraic equations. In 1498, the + and - signs appeared for the first time. The root sign was formulated in 1526. The greater than (>) and less than (<) symbols were created in 1631. The multiplication symbol (x) came about in 1637. In 1650, exponents were formulated (Instead of multiplying the number by so many times). Negative exponents were not used until 1656.

Decimal Numbers (16th Century A.D.) Up until the end of the 16th century the system of base 10 had only been developed for whole numbers. Numbers between whole numbers were expressed as fractions over the base of 60. In 1579, Francois Viete suggested placing fractions of whole numbers over the bases 1000, 100 and 10.

Complex Numbers (16th Century A.D.) Raphael Bombelli gave the first definition of complex numbers, which he called "impossible" or "imaginary" numbers. This introduced the concept of (root -1). A complex number is the sum of a real number and an imaginary one, i.e. a + b(root -1)

Co-ordinates (17th Century A.D.) In the 17th century, univocal locations of a point on a surface were first used in a systematic way to solve geometric problems. This discovery allowed geometric problems to be solved using algebraic techniques. This began a new branch of mathematics - analytical geometry - which linked equations with curves.

Logarithms (17th Century A.D.) John Napier gave the world logarithms in 1614 while doing research on a new method to perform numerical calculations. His system allows the replacement of multiplication with addition and divisions with subraction. (For example, log 10 x log 3 can be re-written as log 13). He found his results to continue to be difficult and formulated the theory of log (base 10) in which any number can be found. Using his method, he calculated the first 31,000 numbers to 14 decimal places.