Mathematics Subject Classification

The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme collaboratively produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH. It 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 MSC2010.

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:

At the top level 64 mathematical disciplines are labeled with a unique 2 digit number. As well as 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:

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:

In addition the special second level code "-" is used for specific kinds of materials. These codes are of the form:

The second and third level of these codes are always the same - only the first level changes. For example, it is not valid to use 53- as a classification. Either 53 on its own or, better yet, a more specific code should be used.

Third level codes are the most specific, usually corresponding to a specific kind of mathematical object or a well-known problem or research area.

The third-level code 99 exists in every category and means none of the above, but in this section

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