Notacionin

Notacionin is a proposed universal mathematical notation framework intended to standardize notation across mathematics and related fields, while remaining readable by humans and machine-processable. It unifies algebra, calculus, logic, and data structures by a common core of symbols and rules.

Development: Emerging from discussions in the 2020s among mathematicians and computer scientists, Notacionin builds on prior notation standardization efforts and on formal language theory. It is designed as modular, with a minimal core and domain-specific extensions.

Features: Core features include a small, orthogonal symbol set, explicit typing, and a formal grammar that governs expression formation. It supports function definition, quantifiers, set notation, and matrix-like structures, with semantics defined by an accompanying formal model.

Syntax and usage: Notacionin favors a clear separation between definition and use, using definitions with an := or other definitional operator, and expression definitions to indicate binding. It aims to be friendly to parsing by software and to minimize ambiguity among disciplines.

Examples and scope: Examples include a simple function f defined by f(x) := x^2 and a quantifier-based statement ∀x ∈ R, x^2 ≥ 0, translated into Notacionin with consistent syntax. The system also provides conventions for indexing, subscripts, and relational operators.

Reception and impact: While praised for potential clarity and cross-disciplinary communication, critics point to the learning curve and the challenge of retrofitting existing textbooks and software. As of now, Notacionin remains an exploratory framework with limited adoption.