ISO 80000-2:2019

Overview

ISO 80000-2:2019 - Quantities and units - Part 2: Mathematics is an international standard that defines mathematical symbols, their meanings, verbal equivalents and typical applications. Primarily intended for the natural sciences and technology, it also applies wherever consistent mathematical notation is required. This second edition (2019) replaces the 2009 edition and provides editorial and technical clarifications on notation, font use and presentation rules.

Key topics and technical requirements

The standard organizes symbols and expressions into topical tables and gives guidance rather than exhaustive definitions. Major technical topics include:

• Variables, functions and operators: conventions for italic vs upright type (e.g., variables in italic, mathematical constants and well‑defined operators in upright), spacing rules around binary and unary operators, and rules for function arguments and parentheses.
• Mathematical logic and sets: symbols for conjunction, disjunction, quantifiers, membership, unions, intersections, Cartesian products, power sets and cardinality.
• Standard number sets and intervals: notation for natural numbers, integers, reals, intervals and related set notation.
• Elementary geometry, operations and combinatorics: common geometric symbols, algebraic operations and combinatorial notation.
• Functions and special functions: notation for general functions, exponentials, logarithms, circular and hyperbolic functions, and special functions.
• Complex numbers, matrices, coordinate systems, transforms and tensors: standardized symbols and brief usage remarks for multivariable and applied-mathematical structures.
• Presentation rules: guidance on line breaks in long expressions, use of thin spaces around binary operators, and table formatting (e.g., Table 13 for coordinate symbols and differentials).

Note: entries in ISO 80000-2 are primarily for identification and readability; the tables give remarks and examples but are not exhaustive mathematical definitions.

Applications and practical value

ISO 80000-2 helps ensure consistent mathematical notation across disciplines and documents, which improves clarity, interoperability and technical communication. Typical applications:

• Scientific and engineering publications, research papers and technical reports
• Standards development and normative documents requiring consistent symbols
• Technical editing, typesetting and academic publishing (font and spacing rules)
• Software documentation, APIs and data exchange formats where notation must be unambiguous
• Education materials and multilingual documents to harmonize verbal equivalents

Who should use this standard

• Scientists, engineers and researchers
• Standards writers and technical committees
• Technical editors, publishers and typesetters
• Software architects and documentation teams handling scientific computation
• Educators and translators of STEM content

Related standards

• ISO 80000-1 - Quantities and units - Part 1: General (normative reference)
• Other parts of the ISO 80000 series and the corresponding IEC 80000 series for related domains (see ISO and IEC websites)

Keywords: ISO 80000-2:2019, mathematical symbols, quantities and units, notation standard, scientific notation, technical notation, mathematical operators, sets, functions, tensors.