The history of mathematical notation covers the introduction, development, and cultural diffusion of mathematical symbols and the conflicts between notational methods that arise during a notation's move to popularity or obsolescence. 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 variety of symbols invented by mathematicians over the past several centuries.

The historical development of mathematical notation can be divided into three stages:

The more general area of study known as the history of mathematics 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.

Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures. For example, geometry has its origins in the calculation of distances and areas in the real world; algebra started with methods of solving problems in arithmetic. The earliest mathematical notations emerged from these problems.

There can be no doubt that most early peoples who left records knew something of numeration and mechanics and that a few were also acquainted with the elements of land-surveying. In particular, the ancient Egyptians paid attention to geometry and numbers, and the ancient Phoenicians performed practical arithmetic, book-keeping, navigation, and land-surveying. The results attained by these people seem to have been accessible (under certain conditions) to travelers, facilitating dispersal of the methods. It is probable that the knowledge of the Egyptians and Phoenicians was largely the result of observation and measurement, and represented the accumulated experience of many ages. Subsequent studies of mathematics by the Greeks were largely indebted to these previous investigations.

Written mathematics began with numbers expressed as tally marks, with each tally representing a single unit. Numerical symbols consisted probably of strokes or notches cut in wood or stone, which were intelligible across cultures. For example, one notch in a bone represented one animal, person, or object. Numerical notation's distinctive feature—symbols having both local and intrinsic values—implies a state of civilization at the period of its invention.

The earliest evidence of written mathematics dates back to the ancient Sumerians and the system of metrology from 3000 BC. From around 2500 BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of Babylonian numerals also date back to this period. Babylonian mathematics has been reconstructed from more than 400 clay tablets unearthed since the 1850s. Written in cuneiform, these tablets were inscribed whilst the clay was soft and then baked hard in an oven or by the heat of the sun. Some of these appear to be graded homework.^{[citation needed]}

The majority of Mesopotamian clay tablets date from 1800 to 1600 BC, and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of regular numbers, reciprocals, and pairs. The tablets also include multiplication tables and methods for solving linear and quadratic equations. The Babylonian tablet YBC 7289 gives an approximation of √2 that is accurate to an equivalent of six decimal places.