Events relating to mathematics
Numbers are written in Egyptian records using the decimal system, on the same principle as that used much later in Rome

The Rhind Mathematical Papyrus, copied out by Ahmes, an Egyptian scribe, offers some of the world's first exam questions
Mathematicians in both Babylon and Egypt independently calculate Π to within 1% of the true value
The Babylonians introduce an important step in the story of arithmetic - the concept of place value in numbers, with digits on the left having greater value than those on the right
Egyptian accountants and architects have a symbol for zero, used not as a numeral but as the base line for larger or physically higher units
The abacus is used as an everyday method of calculation by Phoenicians and Babylonians
The Greek mathematician Pythagoras establishes himself, along with his followers, in southern Italy
The followers of Pythagoras discover the mathematical basis of the octave
The Romans evolve a system of numerals which, until the end of the Middle Ages, is a handicap to western arithmetic
The Greek mathematician Eratosthenes calculates the circumference of the world with the help of shadows and camels
Liu Hui writes a detailed commentary on the Chinese mathematical text Nine Chapters on the Mathematical Art, which includes a discussion of negative numbers
The Lokavibhaga, an Indian Jain text, contains the earliest known reference to the numeral zero being used in place-value notation
The ten-digit numeral system (1-9 with O) is introduced in India, though now most widely known as Arabic numerals
The use of zero, essential in practical mathematics, is now familiar in India and is adopted in Baghdad
Omar Khayyám, mathematician and astronomer, writes four-line verses, or quatrains, in his spare time
Fibonacci uses Arabic numerals in his Liber Abaci ('Book of the Abacus') and thus contributes greatly to their spread in Europe
In Minfici Logarithmorum Canonis DescriptioJohn Napier describes the functioning of his logarithms as a useful mathematical tool
Fermat writes in the margin of a book a mathematical theorem of which he says he has proof, which taunts mathematicians until finally proved in 1995
Galileo's Discorsi, published in Leiden, lays the groundwork for mathematical physics
A correspondence between Pascal and Fermat on probability lays the groundwork for the probability theory
Gottfried Wilhelm Leibniz publishes his account of calculus, simultaneously described in manuscript by Newton, but it is Leibniz who publishes first and names the new method
Newton publishes Principia Mathematica, proving gravity to be a constant in all physical systems
The French scientist Denis Papin, while professor of mathematics at Marburg, develops the first steam engine to use a piston
In his Seven Bridges of K&oulm;nigsberg the Swiss mathematician Leonhard Euler lays the basis for the subsequently important mathematical discipline of topology
Euler, the most prolific mathematician in history, dies after a brilliant career that is unhindered by fifteen years of almost total blindness