# The History of Mathematics

### For countless thousands of years mankind has had a fascination with his environment, trying to find reason, meaning and purpose in all that is – and then exploiting it.

This desire, or obsession, to understand and achieve continues to influence our lives to this day – perhaps increasingly so as our reliance on technology accelerates. Where, when and why it all began we can only guess – but here's a brief progress report so far:

**Circa 30,000BC**

Palaeolithic peoples in Europe record numbers on bones.

**Circa 5000BC**

A decimal number system is in use in Egypt.

**Circa 3400BC**

The first number symbols, simple straight
lines, are used in Egypt.

**Circa 3000BC**

The abacus is used in the Middle East and Mediterranean
areas.

**Circa 1850BC**

Babylonians know Pythagoras's Theorem.

**Circa 1800BC**

Babylonians use multiplication tables.

**Circa 1400BC**

A decimal number system, with no zero,
is used in China

**530BC**

Pythagoras of Samos moves to Croton in Italy and teaches
mathematics, geometry, music – and reincarnation.

**Circa 450BC**

Greeks begin to use written numerals.

**Circa 290BC**

Aristarchus of Samos uses a geometric method to calculate
the distance of the Sun and the Moon from Earth. He also proposes
that the Earth orbits the Sun.

**Circa 250BC**

Archimedes gives the
formulae for calculating the volume of a sphere and
a cylinder. He also gives an approximation
of the value of π.
He studies hydrostatics and explains what is now called "Archimedes'
principle".

**127BC**

Hipparchus discovers the precession of the equinoxes
and calculates the length of the year to within 6.5
minutes of the correct value. He uses an early form
of trigonometry in his astronomical work.

**Circa 1AD**

Liu Hsin, a Chinese mathematician uses decimal fractions.

**Circa 700**

Mathematicians in the Mayan civilization introduce a
symbol for zero into their number system.

**Circa 810**

The 'House of Wisdom' is established in Baghdad, where
Greek and Indian mathematical and astronomical works
are translated into Arabic.

**950**

Gerbert of Aurillac (later Pope Sylvester II) reintroduces
the abacus into Europe. He uses Indian/Arabic numerals without
having a zero.

**976**

Codex Vigilanus is copied in Spain and contains the first
evidence of decimal numbers in Europe.

**1072**

Al-Khayyami (Omar Khayyam) writes Treatise
on Demonstration of Problems of Algebra which contains
a complete classification of cubic equations with geometric
solutions found by means of intersecting conic sections. He measures
the length of the year to be 365.24219858156 days.

**Circa 1200**

The Chinese start to use a symbol for zero.

**1202**

Fibonacci (Leonardo of Pisa) writes Liber abaci (The
Book of the Abacus), which sets out the arithmetic and algebra
he had learnt in Arab countries. It also introduces
the famous sequence of numbers now called the "Fibonacci sequence".

**1248**

Li Yeh writes a book which contains negative numbers,
denoted by putting a diagonal stroke through the last digit.

**1336**

Mathematics becomes a compulsory subject for a degree
at the University of Paris.

**1489**

Widman writes an arithmetic book in German which contains
the first appearance of + and - signs.

**1514**

Vander Hoecke uses the + and - signs.

**1606**

Snell makes the first attempt to measure a degree of
the meridian arc on the Earth's surface, and so determine the size
of the Earth.

**1612**

Bachet publishes a work on mathematical puzzles and tricks
which will form the basis for almost all later books on mathematical
recreations. He devises a method of constructing magic squares.

**1614**

Napier publishes his work on logarithms.

**1617**

Napier invents Napier's bones, consisting of numbered
sticks, as a mechanical calculator.

**1626**

Albert Girard publishes a treatise on trigonometry containing
the first use of the abbreviations sin, cos, tan. He
also gives formulae for the area of a spherical triangle.

**1631**

Harriot's contributions are published ten years after
his death in Artis analyticae praxis (Practice of the Analytic
Art). The book introduces the symbols > and < for "greater
than" and "less than" but these symbols are due
to the editors of the work and not Harriot himself.

**1642**

Pascal builds a calculating machine to help his father
with tax calculations. It performs only additions.

**1659**

Rahn publishes Teutsche algebra which contains ÷ (the division
sign) probably invented by Pell.

**1706**

Jones introduces the Greek letter π to represent the ratio of
the circumference of a circle to its diameter.

**1707**

Newton publishes Arithmetica universalis (General Arithmetic)
which contains a collection of his results in algebra.

**1753**

Simson notes that in the Fibonacci sequence the ratio
between adjacent numbers approaches the golden ratio.

**1783**

Royal Society of Edinburgh is founded.

**1815**

Peter Roget (the author of Roget's Thesaurus) invents the "log-log" slide
rule.

**1823**

Babbage begins construction of a large "difference engine" which
is able to calculate logarithms and trigonometric functions. He was
using the experience gained from his small "difference engine" which
he constructed between 1819 and 1822.

**1847**

Boole publishes The Mathematical Analysis of Logic, in
which he shows that the rules of logic can be treated
mathematically rather than metaphysically. Boole's work lays the
foundation of computer logic.

**1848**

Thomson (Lord Kelvin) proposes the absolute temperature
scale now named after him.

**1858**

Möbius describes a strip of paper that has only one side and
only one edge. Now known as the "Möbius strip", it
has the surprising property that it remains in one piece when cut
down the middle. Listing makes the same discovery in the same year.

**1859**

Mannheim invents the first modern slide rule that has
a "cursor" or "indicator".

**1864**

London Mathematical Society founded.

**1867**

Moscow Mathematical Society is founded.

**1872**

Société Mathématique de France is founded.

**1881**

Venn introduces his "Venn diagrams" which become a useful
tools in set theory.

**1883**

The Edinburgh Mathematical Society is founded.

**1890**

St Petersburg Mathematical Society is founded.

**1901**

Planck proposes quantum theory.

**1905**

Einstein publishes the special theory of relativity.

**1907**

Einstein publishes his principle of equivalence, in which
says that gravitational acceleration is indistinguishable from
acceleration caused by mechanical forces. It is a key ingredient
of general relativity.

**1908**

Hardy and Weinberg present a law describing how the proportions
of dominant and recessive genetic traits would be propagated in
a large population. This establishes the mathematical basis for
population genetics.

**1915**

Einstein submits a paper giving a definitive version
of the general theory of relativity.

**1922**

Richardson publishes Weather Prediction by Numerical
Process. He is the first to apply mathematics, in particular the
method of finite differences, to predicting the weather. The calculations
are prohibitive by hand calculation and only the development of
computers will make his idea a reality.

**1935**

Church invents "lambda calculus" which today is an invaluable
tool for computer scientists.

**1948**

Norbert Wiener publishes Cybernetics: or, Control and
Communication in the Animal and the Machine. The term "cybernetics" is
due to Wiener. The book details work done on the theory of information
control, particularly applied to computers.

**1948**

Shannon invents information theory and applies mathematical
methods to study errors in transmitted information. This becomes
of vital importance in computer science and communications.

**1949**

Mauchly and John Eckert build the Binary Automatic Computer
(BINAC). One of the major advances of this machine is that data
is stored on magnetic tape rather than on punched cards.

**1975**

Mandelbrot publishes Les objets fractals, forme, hasard
et dimension which describes the theory of fractals.

**1982**

Mandelbrot publishes The fractal geometry of nature which
develops his theory of fractal geometry more fully than his work
of 1975.

### Would you like to learn more?

The information above has been extracted from a chronology compiled by The University of St. Andrews, Scotland. To explore the complete listing click here.

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