The symbolic encoding of mathematical objects and numerical quantities, ideally with the intentions of clarity, easy manipulation, and argumentation. The use of Arabic numerals was a marked improvement over Roman numerals for calculations. Viète’s introduction of letters to represent variables in the 16th century simplified algebraic arguments (see algebra). Euler introduced or popularized the use of many now standard symbols in the 18th century. Set theoretic and logical notation (see logic) appeared in the late 19th and early 20th centuries.

For tables of commonly used mathematical symbols, see Symbols and abbreviations.