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Instructions for using the
Mathematics Subject Classification

Purpose of classification

These instructions apply uniformly to all fields listed. The main purpose of the classification is to help readers to find the items of present or potential interest to them as readily as possible---in MR, in Zbl, or anywhere else where this classification system is used. The review of a paper or book should be printed in the section where it will receive the broadest attention from all readers possibly interested in it - these include both people working in that area and people who are familiar with that area and apply its results and methods elsewhere (inside or outside of mathematics). It will be extremely useful for both readers and classifiers to familiarize themselves with the entire classification system and thus to become aware of all the classifications of possible interest to them.


Every paper or book reviewed in Zbl./MR receives precisely one "primary" classification number, which is simply the number of the section in which the review of the item will be printed. This section should be the one that covers the principal contribution. When a paper contains several principal contributions in different areas, the primary classification should cover the "most important" among them. A paper or book may receive one or several "secondary" classification numbers (or "cross-references"), to cover any remaining principal contributions, ancillary results, motivation or origin of the problems discussed, intended or potential field of application, or other significant aspects worthy of notice.

The "primary" principal contribution is meant to be the one including the most important part of the work actually done in the paper. For example, a paper whose main overall content is the solution of a problem in graph theory, which arose in computer science and whose solution is (perhaps) at present only of interest to computer scientists, belongs primarily in 05C with a cross-reference in 68; conversely, a paper whose overall content lies mainly in computer science should receive a primary classification in 68, even if it makes heavy use of graph theory and proves several new graph-theoretic results along the way.

For an item with its primary classification in an "applied" section (68 through 94), it is recommended that a cross-reference be given to any "pure" mathematics section (00 through 65) to which the item being classified makes a contribution.

Cross references

There are two types of cross-references given after many classifications in the list. The first type is of the form "[For A, see X]"; if this appears in section Y, it means that for contributions described by A one should usually assign the classification X, not Y. The other type of cross-reference merely points out related classifications; it is of the form "[See also ...]","[See mainly ...]", etc., and the classifications listed in the brackets may, but need not, be added to the classification of a paper, or they may be used in place of the classification where the cross-reference is given. The classifier will have to judge which classification is the most appropriate for the paper at hand.

Abel prize 2010
I. M. Gelfand 1913-2009

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