# Timeline of numerals and arithmetic

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A timeline of numerals and arithmetic

## 1000–1500

• 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. 
• 12th century — Indian numerals have been modified by Persian mathematicians 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 — Ghiyath al-Kashi “contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as pi. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating nth roots which is a special case of the methods given many centuries later by Ruffini and Horner.” He is also the first to use the 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 — Ibn al-Banna and al-Qalasadi introduced symbolic notation for algebra and for mathematics in general. 
• 1427 — Al-Kashi completes The Key to Arithmetic containing work of great depth on 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.

## Related Research Articles Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today.

The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation. The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars. A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a numeral is not clearly distinguished from the number that it represents. Liber Abaci is a historic 1202 Latin manuscript on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci.

A numerical digit is a single symbol used alone or in combinations, to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits. Brahmagupta was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the Brāhmasphuṭasiddhānta, a theoretical treatise, and the Khaṇḍakhādyaka, a more practical text. Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus. Positional notation usually denotes the extension to any base of the Hindu–Arabic numeral system. More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred. In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string.

The timeline below shows the date of publication of possible major scientific breakthroughs, theories and discoveries, along with the discoverer. This article discounts mere speculation as discovery, although imperfect reasoned arguments, arguments based on elegance/simplicity, and numerically/experimentally verified conjectures qualify. The timeline begins at the Bronze Age, as it is difficult to give even estimates for the timing of events prior to this, such as of the discovery of counting, natural numbers and arithmetic.

Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics, important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, and Varāhamihira. The decimal number system in use today was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of zero as a number, negative numbers, arithmetic, and algebra. In addition, trigonometry was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.

This timeline of science and engineering in the Muslim world covers the time period from the eighth century AD to the introduction of European science to the Muslim world in the nineteenth century. All year dates are given according to the Gregorian calendar except where noted.

The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205". The Hindu–Arabic numeral system or Indo-Arabic numeral system is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world.

The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness. Mathematical notation comprises the symbols used to write mathematical equations and formulas. Notation generally implies a set of well-defined representations of quantities and symbols operators. The history includes Hindu–Arabic numerals, letters from the Roman, Greek, Hebrew, and German alphabets, and a host of symbols invented by mathematicians over the past several centuries.

A timeline of algebra and geometry

This is a timeline of pure and applied mathematics history. It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic" stage, in which comprehensive notational systems for formulas are the norm. In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length, no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.

1. Rudman, Peter Strom (2007). How Mathematics Happened: The First 50,000 Years. Prometheus Books. p.  64. ISBN   978-1-59102-477-4.