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Mathematics Subject Classification Scheme Revision 2000

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THE REVISION OF THE MATHEMATICS SUBJECT CLASSIFICATION
              --  Principles to use in creating MSC 2000  --
           (A minor revision of the principles of January 1987)


Abbreviations:  
     MSC = Mathematics Subject Classification; 
     ZM = Zentralblatt fuer Mathematik; 
     MR = Mathematical Reviews


          BASIC CONSIDERATIONS FOR REVISING THE MSC

(A)  Functions of the MSC.

        The MSC has three functions:
     (1) It is an essential retrieval aid for online services, searches in
         data bases, profile services, etc.
     (2) It serves as an ordering device for use in review journals,
         special index and reference services, subject indexes, libraries, 
         publishing houses, etc.--i.e., it serves for sorting and
         inventory.
     (3) It has a descriptive function.  It can be used to label the
         subjects discussed in a paper or book and to indicate the 
         mathematical interests of a person.


(B)  Structure and objectives of the MSC scheme.

        In order to be truly useful in all three functions, the MSC has to
satisfy  the following two conditions:
      (I) It must be "stable", so as to serve the needs of data bases and
          their users. Ideally this would mean that the division into broad 
          areas of mathematics should remain unchanged, that structural 
          changes in individual areas be quite limited, and that any 
          changes be made only at large time intervals. 
     (II) It must "reflect reality" and continue to evolve with the
          (sometimes rapid) development of mathematics itself.
A reasonable compromise between these two seemingly conflicting goals
must and can be found.

         Radical or large-scale changes in the structure of the MSC, such as 
     (a) a completely new classification in an existing area, e.g.,
         the change from 10 in the 1980 scheme to 11 in the 1991 scheme
     (b) the organization of a subject that had previously been scattered
         over many of the existing MSC areas into a new, unified area 
         (e.g., the introduction of K-theory, section 19, in 1991),
should be kept to a minimum. However, such major changes ought to be
considered  seriously whenever all of the following three conditions are satisfied:  
     (i) There is a genuine, documented mathematical need for the new 
         arrangement.  
    (ii) A new classification for the area involved, in a form and with 
         a degree of refinement usable for ZM and MR, is prepared by
         people working in that field, and is made available for use in 
         the MSC.  
   (iii) The creators of the classification mentioned in (ii) prepare 
         a two-way conversion table between the old and new versions.
    
        Presumably there is no genuine practical need to condense areas in which 
there is little activity at present.  If an area is to be "absorbed" into
another, this can be accomplished by writing down the necessary
correspondence table.  
        Changes within individual areas should be made only where absolutely
necessary, and the structure of the classifications should be preserved
as much as possible.  In cases where new topics have evolved and are the
subject of significant research activity, or where several different
topics were heretofore listed in the MSC under a single 5-place entry,
new 5-place entries need to be created.
        In general, the MSC is intended to serve the needs of ZM and MR and
their users.  If, for the purpose of publishing a volume of collected
reviews in a particular area (or for some other purpose), the need for a
classification finer than in the MSC arises, it is recommended that one
start with the corresponding part of the MSC, and then refine that by
adding something appropriate after the fifth place.  In some cases, if
this area is a new one not explicitly represented in the MSC system, then
a new entry would need to be created.
        In order to maintain the stability of the MSC as much as possible,      
major revisions should be carried out only at large time intervals.  In
the course of one of these large time intervals, all existing 5-place
classifications should be kept and new ones introduced only when
absolutely necessary.  Moreover, these new, intermediate (or temporary)
5-place entries may be available only in the form of "secondary" or
additional classifications, so that each item has to be classified
completely in terms of the original MSC version in force for the large
time period in question.  

Suggestions for adding new 5-digit classifications will ususally be
considered only when there have been at least 50 papers within the
immediately preceding 3-year period that would have been classfied with
the new classification as primary.


(C)  Criteria for using MSC designations.

(1)  A publication is to be given a particular MSC designation if:
     (a) one of the main concerns or contributions of that publication is
         in the field classified by this designation, or
     (b) results and methods from the field classified by this designation
         are applied in a nontrivial and essential way in the publication 
         in question.
(2)  For additional information or aspects in a publication, e.g., motivation 
     or origin of the problems discussed, intended or potential field of 
     application, not of central interest, it is preferable that one use 
     appropriately chosen key words (or rely on online word search of the text 
     of the reviews). Of course carefully chosen MSC designations may also 
     be used.  

        These conditions are imposed so as to specify the substance of a
publication as accurately and efficiently as possible for  retrieval
purposes.
        The "primary classification" of a publication is simply the most
important one of the designations under (1a), or in special cases perhaps
of those under (1b).  All other designations given to the publication are
"secondary".  All publications must receive a complete classification
under the terms of (1); temporary new designations (e.g., before the 1991
revision,  publications involving K-theory with designations from 19-XX) 
are to be used only in addition to the ones given under (1).
        As indicated above, complete two-way correspondence tables between the
old and the new MSC are to be established and published.  This will be
helpful for any project of reclassifying a complete mathematics data base,
and also for individual users of data bases such as MathSci and MATH in
their present forms.  


(D)  Time constraints.

     The revision of the 1991 scheme now being planned should be
ready for use in the January 2000 issues of MR and ZM.  It should
preferably be ready for use in database production during 1999.


(E)  Summary of the goals and criteria for revising the MSC.

(1)  The revision will be carried out in a way that permits a complete
     correspondence table between the old and the new version to be 
     established.
(2)  The structure of the MSC is to remain unaltered as much as possible;
     changes in structure are subject to specific conditions:
     (a) Existing MSC areas (labeled by the first two digits) should be
         preserved, except in situations where the ongoing development of
         mathematics has necessitated a change and where a suitable new
         classification is supplied by people working in the field in 
         question.
     (b) New 5-place designations should be compatible with the present
         MSC.  New topics should be accepted into the MSC only when there 
         is significant activity in them.
     (c) "Refining" existing portions of the MSC is to proceed in two
         ways:  In some places it may be necessary to break up an
         existing letter section; the hope is that there will be very 
         few such places.  Different topics listed until now together 
         under a single 5-place designation will get their own 5-place 
         designations.  Closely related topics listed in a single 5-place 
         entry will stay there and may be distinguished by specifying
         suitable key words in the descriptive text.
     (d) The descriptive texts of 5-place entries will be revised so as to 
         facilitate retrieval in data bases.  Routine enumerations
         will be eliminated by splitting designations as described in (c), or 
         by rewriting the description and hiding the list of terms.  
         (The texts should ideally be intelligible and unambiguous 
         without having to look up at the ***xx or **-XX
         designations, though this needs to be balanced against the
         succinctness desired.)
     (e) Cross references between "competing" 5-place designations should
         be improved.  
     (f) Other classification standards in areas where mathematics is
         applied or even created should be taken into consideration as 
         much as possible, subject to the limitations described above.
     (g) MR and ZM will attempt to attain a close-to-uniform degree of
         fineness of the classification in all areas.  That is, at both 
         of the second and third levels the classification should roughly 
         be "equally fine" for all entries, to the extent that this is 
         possible to achieve. 
(3)  The new MSC scheme will be acccepted as a common standard for the
     mathematical community.  Future changes are to be made only after 
     joint agreement between MR and ZM has been reached.

 [revision of 01 September 1995]


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