The Fulltext UNESCO Nomenclature

Algorithms, Artificial Intelligence (AI), Information Architecture, Mathematics, Open Data, Open Innovation, Research and Development, Software, Standards

The “UNESCO Nomenclature for Fields of Science and Technology” is a hierarchical classification system developed by the United Nations Educational, Scientific and Cultural Organization to categorize research papers and doctoral dissertations. Initially proposed in the early 1970s, this system provides a standardized method for organizing scientific and technological information. It is structured into three levels of detail, identified by 2-digit, 4-digit, and 6-digit codes, which correspond to fields, disciplines, and sub-disciplines respectively. This systematic organization allows for the precise classification of a wide array of research activities. The nomenclature is a widely used tool in the management of knowledge for research projects and academic theses.

The structured nature of the UNESCO Nomenclature offers significant potential for applications beyond academia and scientific research, extending into innovation and marketing. The nomenclature can be used to map existing innovation domains or datas, and classifying opportunities for novel technological development. For marketers, it can help in segmenting technology-driven markets and understanding the scientific foundations of products to craft more precise messaging.

The full 18 pages original pdf document can be found here: UNESCO Nomenclature.

Over the years, the original online, archived or updated versions of the UNESCO Nomenclature have appeared and disappeared (Unesco’s itself, later the EU and Eurostat) including their copyright notice. The most maintained and useful being now the work of SKOS at the University of Murcia (Spain), from which this version is derived from.

Why do we provide it here: because it’s complete, well taught and we use it extensively ourselves (see all our inventions and innovations directory and posts for example), and the following list is way more usable and searchable than the old scanned paper pdf version. Thanks to the UNESCO and the SKOS group for that work, provided (likely?) under CC BY 4.0.

Note that the 6 digits subcategories:

never use fully all 1-99 combinations of the last 2 digits, leaving room for futur subcategories completion.
that there is always a “.99: Others (specify)” to be already used currently until more subcategories are officially added.

11: Logic

1101: Applications of logic

1102: Deductive Logic

1102.01: Analogy
1102.02: Boolean Algebra
1102.03: Formal Logic
1102.04: Formalized languages
1102.05: Formal systems
1102.06: Foundations of mathematics
1102.07: Generalization
1102.08: Mathematical logic
1102.09: Modal Logic
1102.10: Model theory
1102.11: Proff theory
1102.12: Propositional Calculus
1102.13: Recursive functions
1102.14: Symbolic logic
1102.15: Theory of formal languages
1102.99: Other (specify)

1103: General Logic

1104: Inductive Logic

1104.01: Induction
1104.02: Intuitionism
1104.03: Probability
1104.99: Other (specify)

1105: Methodology

1105.01: Scientific method
1105.99: Other (specify)

1199: Other specialties on logic (specify)

12: Mathematics

1201: Algebra

- 1201.01: Algebraic geometry
- 1201.02: Axiomatic set theory
- 1201.03: Category theory
- 1201.04: Differential algebra
- 1201.05: Fields, rings, algebra
- 1201.06: Groups, generalizations
- 1201.07: Homological algebra
- 1201.08: Lattices
- 1201.09: Lie algebra
- 1201.10: Linear algebra
- 1201.11: Matrix theory
- 1201.12: Non-associative algebras
- 1201.13: Polynomials
- 1201.14: Representation theory
- 1201.99: Other (specify)

1202: Analysis and functional analysis

1202.01: Algebra of operators
1202.02: Approximation theory
1202.03: Banach spaces and algebras
1202.04: Calculus of variations
1202.05: Combinatorial analysis
1202.06: Convexity, Inequalities
1202.07: Difference equations
1202.08: Functional equations
1202.09: Functions of a complex variable
1202.10: Functions of real variables
1202.11: Functions of several complex variables
1202.12: Global Analysis
1202.13: Harmonic analysis
1202.14: Hilbert Spaces
1202.15: Integral equations
1202.16: Integral transforms
1202.17: Measure, integration, area
1202.18: Operational calculus
1202.19: Ordinary differential equations
1202.20: Partial differential equations
1202.21: Potential theory
1202.22: Series, summability
1202.23: Special functions
1202.24: Subharmonic functions
1202.25: Topological linear spaces
1202.26: Trigonometric series and integrals
1202.99: Other (specify)

1203: Computer Sciences

1203.01: Accounting
1203.02: Algorithmic languages
1203.03: Analog computing
1203.04: Artificial Intelligence
1203.05: Automated manufacturing systems
1203.06: Automated quality control systems
1203.07: Causal modelling
1203.08: Codes and coding systems
1203.09: Computer-assisted design
1203.10: Computer-assisted instruction
1203.11: Computer software
1203.12: Data banks
1203.13: Digital computing
1203.14: Environmental control systems
1203.15: Heuristics
1203.16: Hybrid computing
1203.17: Informatics
1203.18: Information systems and components; design and components
1203.19: Inventory Control
1203.20: Medical monitoring systems
1203.21: Navigation and space telemetry systems
1203.22: Production control systems
1203.23: Programming languages
1203.24: Programming theory
1203.25: Sensors systems design
1203.26: Simulation
1203.99: Other (specify)

1204: Geometry

1204.01: Affine geometry
1204.02: Complex manifolds
1204.03: Convex domains
1204.04: Differential geometry
1204.05: Extremum problems
1204.06: Euclidean geometry
1204.07: Finite geometries
1204.08: Foundations
1204.09: Non-Euclidean geometries
1204.10: Projective geometry
1204.11: Riemannian geometry
1204.12: Tensor Analysis
1204.99: Other (specify)

1205: Number Theory

1205.01: Algebraic numbers theory
1205.02: Analytic number theory
1205.03: Diophantine problems
1205.04: Elementary number theory
1205.05: Geometry of numbers
1205.99: Other (specify)

1206: Numerical Analysis

1206.01: Algorithms construction
1206.02: Differential equations
1206.03: Error analysis
1206.04: Functional Equations
1206.05: Integral equations
1206.06: Integro-differential equations
1206.07: Interpolation, approximation and curve fitting
1206.08: Iterative Methods
1206.09: Linear Equations
1206.10: Matrices
1206.11: Numerical differentiation
1206.12: Ordinary differential equations
1206.13: Partial differential equations
1206.14: Quadratura
1206.99: Other (specify)

1207: Operations Research

1207.01: Activity analysis
1207.02: Control systems
1207.03: Cybernetics
1207.04: Distribution and transport
1207.05: Dynamic programming
1207.06: Game theory
1207.07: Integer programming
1207.08: Inventory
1207.09: Linear programming
1207.10: Networks flow
1207.11: Non-linear Ppogramming
1207.12: Queuing
1207.13: Scheduling
1207.14: Systems formulation
1207.15: Systems reliability
1207.99: Other (specify)

1208: Probability

1208.01: Actuarial mathematics
1208.02: Analytic probability theory
1208.03: Application of probability
1208.04: Foundations of probability
1208.05: Limit theorems
1208.06: Markov processes
1208.07: Plausibility
1208.08: Stochastic processes
1208.09: Subjective probabilities
1208.99: Other (specify)

1209: Statistics

1209.01: Analytical statistics
1209.02: Computing for statistics
1209.03: Data analysis
1209.04: Decision procedures and theory
1209.05: Design and analysis of experiments
1209.06: Distribution-free and nonparametric methods
1209.07: Distribution and probability theory
1209.08: Foundations of statistical inference
1209.09: Multivariate analysis
1209.10: Sampling theory and techniques
1209.11: Stochastic theory and time series analysis
1209.12: Techniques of statistical association
1209.13: Techniques of statistical inferenc
1209.14: Techniques of statistical prediction
1209.15: Time series
1209.99: Other (specify)

1210: Topology

1210.01: Abstract spaces
1210.02: Cohomology
1210.03: Differential manifolds
1210.04: Fibre bundles and spaces
1210.05: General topology
1210.06: Homology
1210.07: Homotopy
1210.08: Lie groups
1210.09: Piecewise linear topology
1210.10: Point-set topology
1210.11: Three dimensional topology
1210.12: Topological groups
1210.13: Topological dynamics
1210.14: Topological embedding
1210.15: Topological manifolds
1210.16: Transformation groups
1210.99: Other (specify)

1299: Other mathematical specialities

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Topics covered: UNESCO Nomenclature, hierarchical classification, scientific research, technological research, standardized method, research papers, doctoral dissertations, innovation domains, technology-driven markets, knowledge management, academic theses, systematic organization, ISO 9001, ISO/IEC 27001, ISO 14001, and ISO 45001..

Historical Context

Study room of Peter Gustav Lejeune Dirichlet with mathematical notes on convergence conditions.

Dirichlet Conditions for Convergence

For a Fourier series to converge to the function's value, the function must satisfy the Dirichlet conditions over one period. These are: (1) the function must be absolutely integrable, (2) it must have a finite number of extrema (maxima and minima), and (3) it must have a finite number of finite discontinuities.

De Morgan’s Laws

De Morgan's laws are a pair of transformation rules in Boolean algebra that are fundamental to digital circuit design. The first law states that the negation of a conjunction is the disjunction of the negations: \(\neg(P \land Q) \iff (\neg P) \lor (\neg Q)\). The second states that the negation of a disjunction is the conjunction of the negations: \(\neg(P \lor Q) \iff (\neg P) \land (\neg Q)\).

Parchment scroll detailing differentiable manifolds in a historical study room.

Differentiable Manifolds (geom)

A differentiable manifold is a topological space that is locally similar to Euclidean space, allowing calculus to be applied. Each point has a neighborhood that is homeomorphic to an open subset of \(\mathbb{R}^n\). These local coordinate systems, called charts, are related by smooth transition functions, forming an atlas that defines the manifold's differentiable structure.

Wooden desk with ledger, quill, and chalkboard showing Boolean algebra logic gates.

Boolean Algebra in Digital Logic

Digital electronics is based on Boolean algebra, a mathematical system of logic introduced by George Boole. It uses two values, typically 0 and 1 (or false and true), and three basic operations: AND (conjunction), OR (disjunction), and NOT (negation). These operations directly correspond to the logic gates that form the building blocks of all digital circuits.

Homeomorphism

A homeomorphism is a continuous function between two topological spaces that has a continuous inverse function. Two topological spaces are called homeomorphic if such a function exists. From a topological viewpoint, homeomorphic spaces are identical. This concept captures the idea that an object can be stretched, bent, or deformed into another without tearing or gluing, like a coffee mug into a donut.

Signal processing laboratory analyzing Fourier series behavior at discontinuities.

Gibbs Phenomenon

The Gibbs phenomenon describes the behavior of a Fourier series at a jump discontinuity. The partial sums of the series exhibit an overshoot near the jump, which does not disappear as more terms are added. This overshoot converges to a constant value of about 9% of the jump height, regardless of the number of terms in the series.

The Gauss-Markov Theorem

This theorem states that in a linear regression model where the errors have zero mean, are uncorrelated, and have constant variance (homoscedasticity), the ordinary least squares (OLS) estimator is the Best Linear Unbiased Estimator (BLUE). 'Best' means it has the minimum variance among all linear unbiased estimators of the regression coefficients, making it the most precise.

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George Green working on the fundamental solution in a historical office setting, mathematical physics.

Fundamental Solution (Green’s Function)

A fundamental solution of a linear partial differential operator \(L\) is a solution to the equation \(Lu = delta(x)\), where \(delta(x)\) is the Dirac delta function. It represents the response of the system to a point source or impulse. Once known, the solution to the inhomogeneous equation \(Lu = f(x)\) can be found by convolution: \(u(x) = (G * f)(x)\), where \(G\) is the fundamental solution.

The Gauss-Bonnet Theorem

The Gauss-Bonnet theorem connects the geometry of a compact two-dimensional surface to its topology. It states that the integral of the Gaussian curvature \(K\) over the entire surface \(M\) is equal to \(2\pi\) times the Euler characteristic \(\chi(M)\) of the surface. The formula is \(\int_M K \, dA = 2\pi \chi(M)\).

Precision measuring instruments in a 1850s laboratory for scientific experimentation.

Accuracy vs. Precision

Accuracy refers to the closeness of a measured value to a standard or known true value. Precision refers to the closeness of two or more measurements to each other. A measurement system can be precise but not accurate, accurate but not precise, neither, or both. These two concepts are independent of each other in measurement theory.

Riemannian Geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds—smooth manifolds equipped with a Riemannian metric. This metric is a collection of inner products on the tangent spaces, varying smoothly from point to point. It allows for the definition of local geometric notions like angle, length of curves, surface area, and volume, leading to a generalized notion of curvature.

Rank-Nullity Theorem

In linear algebra, the rank-nullity theorem states that for any linear map \(T: V \to W\) between finite-dimensional vector spaces, the dimension of its domain \(V\) is the sum of its rank (the dimension of its image) and its nullity (the dimension of its kernel). The formula is \(\dim(V) = \text{rank}(T) + \text{nullity}(T)\).

Vintage office with mathematical papers and antique calculator related to prime number theory.

The Prime Number Theorem

The Prime Number Theorem describes the asymptotic distribution of prime numbers among the integers. It states that the prime-counting function \(\pi(x)\), which gives the number of primes less than or equal to \(x\), is asymptotically equivalent to \(x / \ln(x)\). Formally, \(\lim_{x \to \infty} \frac{\pi(x)}{x/\ln(x)} = 1\). This provides a fundamental link between primes and the natural logarithm.

Statistician analyzing regression model data in an office setting.

Coefficient of Determination (R²)

A statistic indicating the goodness of fit of a model, representing the proportion of the variance in the dependent variable that is predictable from the independent variable(s). An R² of 1 indicates a perfect fit, while 0 indicates no linear relationship. It is calculated as \(R^2 \equiv 1 - \frac{SS_{res}}{SS_{tot}}\), where \(SS_{res}\) is the residual sum of squares.

Fredholm Index

The Fredholm index generalizes the rank-nullity theorem to infinite-dimensional spaces like Banach spaces. For a Fredholm operator \(T: X \to Y\), its index is defined as \(\text{ind}(T) = \dim(\ker(T)) - \dim(\text{coker}(T))\), where the Cokernel's dimension measures how far the image is from being the whole space. This index is a stable integer value under small perturbations of the operator.

(if date is unknown or not relevant, e.g. "fluid mechanics", a rounded estimation of its notable emergence is provided)