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The Mathematics Subject Classification (MSC) is a numerical classification scheme formulated by the American Mathematical Society.

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 subject codes so listed are used by the two major reviewing databases, Mathematical Reviews and Zentralblatt MATH.

The Mathematics Subject Classification employs a hierarchical scheme. At the top level, 64 disciplines are distinguished, each labeled by a 2-digit number. For example

• "03" is "Mathematical Logic and Foundations",
• "11" is "Number theory"
• "68" is "Computer Science"
• "92" is "Biology and other natural sciences"

A detailed review of each of the disciplines is provided in the article on areas of mathematics.

Each discipline is then broken down into a handful of subfields; for example,

• subfields of "03" are, among others,
  • "03D Computability and recursion theory"
  • "03E Set theory"
• subfields of "68" are, among others
  • "68Q Theory of computing"
  • "68T Artificial Intelligence"

Finally, each of the subfields may be split into several subjects, each labeled with a 2-digit number; for example,

• a subfield of 03D is
  • 03D10 Turing machines and related notions
• 68Q has currently 18 subfields, among them
  • 68Q05 Models of computation (Turing machines, etc.)
  • 68Q15 Complexity classes
  • 68Q45 Formal languages and automata

However, it is not always clear how to classify a mathematical paper or theorem, as these fields and subjects are far from disjoint. For example, the same (or very similar) questions, concepts and ideas may appear in both "68Q05" (Turing machines from the computer science point of view) and "03D10" (Turing machines from the mathematical point of view).

• Wikipedia uses two different classification schemes: the category system, consisting of the subcategories of Category:Mathematics, and an ad-hoc list of lists of mathematical topics. These systems are intended to assist users of the encyclopedia to browse the available topics. It is therefore based upon less library-science-based criteria, and includes some items that would not fit in the MSC, such as list of exponential topics and list of factorial and binomial topics.
• Subject classes in the arXiv — The classification in the arXiv is chosen to reflect the papers submitted to the arXiv. For this reason, the arXiv has a special class for quantum algebra, which is not mentioned in the MSC. [1]
• The ACM Computing Classification System is a similar hierarchical classification scheme for Computer 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 American Mathematical Society page on the Mathematics Subject Classification. Currently documents the 2000 edition of the MSC together with its changes from the 1991 version, as well as providing some general information about the scheme and its history.
• Description of the MSC by Dave Rusin.

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