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History of mathematical notation
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<p>The history of mathematical notation covers the introduction, development, and <a href="/facts/Cultural_diffusion/EURDJKVV">cultural diffusion</a> of <a href="/facts/Mathematical_symbol/rQkbGGna">mathematical symbols</a> and the conflicts between notational methods that arise during a notation's move to popularity or obsolescence. <a href="/facts/Mathematical_notation/vHgEE8cE">Mathematical notation</a> comprises the symbols used to write mathematical <a href="/facts/Equation/pxFzLAVR">equations</a> and <a href="/facts/Formula/BosTcKnv">formulas</a>. Notation generally implies a set of <a href="/facts/Well-defined/GAc0XbWz">well-defined</a> representations of quantities and symbols operators. The history includes <a href="/facts/Hindu%E2%80%93Arabic_numerals/z73KvotW">Hindu–Arabic numerals</a>, letters from the <a href="/facts/Roman_alphabet/pqWVHpBz">Roman</a>, <a href="/facts/Greek_alphabet/1cHwB8Dg">Greek</a>, <a href="/facts/Hebrew_alphabet/qQStmr5u">Hebrew</a>, and <a href="/facts/German_alphabet/wRfTdcfG">German</a> <a href="/facts/Alphabet/vqfRpS3E">alphabets</a>, and a variety of symbols invented by mathematicians over the past several centuries. </p><p>The historical development of mathematical notation can be divided into three stages: </p> <ul><li><i><a href="/facts/Rhetorical/mB9np26l">Rhetorical</a> stage</i>—where calculations are performed by words and tallies, and no symbols are used.</li> <li><i><a href="/facts/Syncopated/qA2dqkTI">Syncopated</a> stage</i>—where frequently-used operations and quantities are represented by symbolic <a href="/facts/Syntax/6PxSV98p">syntactical</a> abbreviations, such as letters or numerals. During antiquity and the medieval periods, bursts of mathematical creativity were often followed by centuries of stagnation. As the <a href="/facts/Early_modern_age/hhpHM721">early modern age</a> opened and the worldwide spread of knowledge began, written examples of mathematical developments came to light.</li> <li><i>Symbolic stage</i>—where comprehensive systems of notation supersede rhetoric. The increasing pace of new mathematical developments, interacting with new scientific discoveries, led to a robust and complete usage of symbols. This began with mathematicians of medieval India and mid-16th century Europe, and continues through the present day.</li></ul> <p>The more general area of study known as the <a href="/facts/History_of_mathematics/18h5rQA5">history of mathematics</a> primarily investigates the origins of discoveries in mathematics. The specific focus of this article is the investigation of mathematical methods and notations of the past. </p>