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Concept
Mathematics Subject Classification
Summary
The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme that has collaboratively been produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH. The MSC is used by many mathematics journals, which ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The current version is MSC2020.
The MSC is a hierarchical scheme, with three levels of structure. A classification can be two, three or five digits long, depending on how many levels of the classification scheme are used.
The first level is represented by a two-digit number, the second by a letter, and the third by another two-digit number. For example:
53 is the classification for differential geometry
53A is the classification for classical differential geometry
53A45 is the classification for vector and tensor analysis
At the top level, 64 mathematical disciplines are labeled with a unique two-digit number. In addition to the typical areas of mathematical research, there are top-level categories for "History and Biography", "Mathematics Education", and for the overlap with different sciences. Physics (i.e. mathematical physics) is particularly well represented in the classification scheme with a number of different categories including:
Fluid mechanics
Quantum mechanics
Geophysics
Optics and electromagnetic theory
All valid MSC classification codes must have at least the first-level identifier.
The second-level codes are a single letter from the Latin alphabet. These represent specific areas covered by the first-level discipline. The second-level codes vary from discipline to discipline.
For example, for differential geometry, the top-level code is 53, and the second-level codes are:
A for classical differential geometry
B for local differential geometry
C for global differential geometry
D for symplectic geometry and contact geometry
In addition, the special second-level code "-" is used for specific kinds of materials.
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