Timeline of numerals and arithmetic

A timeline of numerals and arithmetic.

Before 2000 BC

• c.
  Ishango Bone: suggested, though disputed, as the earliest reference to prime numbers as also a common number.^[1]
• c. 3400 BC — the Sumerians invent the first so-known numeral system,^{[dubious – discuss]} and a system of weights and measures.
• c. 3100 BC — Egypt, earliest known decimal system allows indefinite counting by way of introducing new symbols, [1].^{[citation needed]}
• c. 2800 BC —
  ancient weights and measures, the smallest unit of measurement used is 1.704 millimetres and the smallest unit of mass used is 28 grams.^{[citation needed}
  ]
• c. 2000 BC —
  Babylonians use a base-60 decimal system, and compute the first known approximate value of π at 3.125.^{[citation needed}
  ]

• c. 1000 BC —
  Vulgar fractions used by the Egyptians
  .
• second half of 1st millennium BC — The
  Lo Shu Square, the unique normal magic square of order three, was discovered in China
  .
• c. 400 BC —
  Jaina mathematicians in India write the “Surya Prajinapti”, a mathematical text which classifies all numbers into three sets: enumerable, innumerable and infinite. It also recognises five different types of infinity
  : infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.
• c. 300 BC —
  Brahmi numerals are conceived in India
  .
• 300 BC —
  Babylonians invent the earliest calculator, the abacus.^{[dubious – discuss][citation needed}
  ]
• c. 300 BC —
  Fibonacci numbers and Pascal's triangle
  .
• c. 250 BC — late
  0 (number)
  .
• 150 BC —
  combinations
  .
• 50 BC —
  base-10 numeral system, begins developing in India
  .

• 300 — the earliest known use of
  Indian mathematicians
  .
• c. 400 — the
  square roots
  of numbers as large as a million correct to at least 11 decimal places.
• 550 —
  Indian numeral
  system.
• 628 —
  square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and the Brahmagupta theorem
  .
• 940 —
  roots
  using the Indian numeral system.
• 953 — The
  Al-Uqlidisi modified these methods for pen and paper use. Eventually the advances enabled by the decimal system
  led to its standard use throughout the region and the world.

• c. 1000 — Pope Sylvester II introduces the abacus using the Hindu–Arabic numeral system to Europe.
• 1030 —
  Ali Ahmad Nasawi writes a treatise on the decimal and sexagesimal number systems. His arithmetic explains the division of fractions and the extraction of square and cubic roots (square root of 57,342; cubic root of 3, 652, 296) in an almost modern manner.^[2]
• 12th century —
  al-Khwārizmī to form the modern Arabic numerals
  (used universally in the modern world.)
• 12th century — the Arabic numerals reach Europe through the Arabs.
• 1202 —
  Leonardo Fibonacci demonstrates the utility of Hindu–Arabic numeral system
  in his Book of the Abacus.
• c. 1400 —
  decimal point notation in arithmetic and Arabic numerals
  . His works include The Key of arithmetics, Discoveries in mathematics, The Decimal point, and The benefits of the zero. The contents of the Benefits of the Zero are an introduction followed by five essays: “On whole number arithmetic”, “On fractional arithmetic”, “On astrology”, “On areas”, and “On finding the unknowns [unknown variables]”. He also wrote the Thesis on the sine and the chord and Thesis on finding the first degree sine.
• 15th century —
  al-Qalasadi introduced symbolic notation for algebra and for mathematics in general.^[3]
• 1427 —
  decimal fractions
  . It applies arithmetical and algebraic methods to the solution of various problems, including several geometric ones.
• 1478 — An anonymous author writes the Treviso Arithmetic.

17th century

• 1614 — John Napier publishes a table of Napierian logarithms in Mirifici Logarithmorum Canonis Descriptio,
• 1617 — Henry Briggs discusses decimal logarithms in Logarithmorum Chilias Prima,
• 1618 —
  logarithms
  .

18th century

• 1758 — Arithmetika Horvatzka, Croatia's first arithmetic textbook is published in Zagreb by Mihalj Šilobod Bolšić (1724–1787).
• 1794 —
  Thesaurus Logarithmorum Completus
  .

Calculation of Pi

• 1706 — John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places.
• 1789 — Jurij Vega improves Machin's formula and computes π to 140 decimal places.
• 1949 — John von Neumann computes π to 2,037 decimal places using ENIAC.
• 1961 — Daniel Shanks and John Wrench compute π to 100,000 decimal places using an inverse-tangent identity and an IBM-7090 computer.
• 1987 —
  NEC SX-2 supercomputer
  to compute π to 134 million decimal places.
• 2002 —
  Hitachi 64-node supercomputer
  .

• Abacus – Calculating tool
• Alphabetic numeral system – Type of numeral system
• Attic numerals – Symbolic number notation used by the ancient Greeks
• Australian Aboriginal enumeration
• Counting rods – East Asian numeral systemPages displaying wikidata descriptions as a fallback
• History of ancient numeral systems – Symbols representing numbers
• History of arithmetic
   – Branch of elementary mathematicsPages displaying short descriptions of redirect targets
• History of mathematics
• History of numbers
   – Used to count, measure, and labelPages displaying short descriptions of redirect targets
• History of the Hindu–Arabic numeral system
• Jeton – Coin-like counting token
• List of numeral system topics
• List of numeral systems
• Number theory – Mathematics of integer properties
• Prehistoric counting
• Relationship between mathematics and physics – Study of how mathematics and physics relate to each other
• Roman numerals – Numbers in the Roman numeral system
• Timeline of algorithms
• Timeline of mathematics

References