TheMathematics Subject Classification (MSC) is an alphanumericalclassification scheme that has collaboratively been produced by staff of, and based on the coverage of, the two major mathematical reviewing databases,Mathematical Reviews andZentralblatt MATH. The MSC is used by many mathematicsjournals, which ask authors ofresearch 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:
At the top level, 63 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 andBiography", "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 is53, 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 use53- as a classification. Either53 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 meansnone of the above, but in this section.
The AMS recommends that papers submitted to its journals for publication have one primary classification and one or more optional secondary classifications. A typical MSC subject class line on a research paper looks like
MSC Primary 03C90; Secondary 03-02;
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According to theAmerican Mathematical Society (AMS) help page about MSC,[1] the MSC has been revised a number of times since 1940. Based on a scheme to organize AMS'sMathematical Offprint Service (MOS scheme), theAMS Classification was established for the classification of reviews inMathematical Reviews in the 1960s. It saw various ad-hoc changes. Despite its shortcomings,Zentralblatt für Mathematik started to use it as well in the 1970s. In the late 1980s, a jointly revised scheme with more formal rules was agreed upon by Mathematical Reviews and Zentralblatt für Mathematik under the new name Mathematics Subject Classification. It saw various revisions asMSC1990,MSC2000 andMSC2010.[2] In July 2016, Mathematical Reviews and zbMATH started collecting input from the mathematical community on the next revision of MSC,[3] which was released as MSC2020[4] in January 2020.
The original classification of older items has not been changed. This can sometimes make it difficult to search for older works dealing with particular topics. Changes at the first level involved the subjects with (present) codes 03, 08, 12-20, 28, 37, 51, 58, 74, 90, 91, 92.
For physics papers thePhysics and Astronomy Classification Scheme (PACS) is often used. Due to the large overlap between mathematics and physics research it is quite common to see both PACS and MSC codes on research papers, particularly for multidisciplinary journals and repositories such as thearXiv.
TheACM Computing Classification System (CCS) is a similarhierarchical classification scheme forcomputer science. There is some overlap between the AMS and ACM classification schemes, in subjects related to both mathematics and computer science, however the two schemes differ in the details of their organization of those topics.
The classification scheme used on the arXiv is chosen to reflect the papers submitted. As arXiv is multidisciplinary its classification scheme does not fit entirely with the MSC, ACM or PACS classification schemes. It is common to see codes from one or more of these schemes on individual papers.
