TITLE: How should the Math Subject Classification (MSC) be revised or improved?
QUESTION [18 upvotes]: Most of us are familiar with the Math Subject
Classification
(MSC),
a coded index attempting to classify all mathematical
research areas by topic. The MSC, devloped jointly by the Math Reviews and Zentralblatt, is used by most journals and many grant institutions,
such as the US National Science Foundation, as a way of
grouping mathematical work into topic categories. The MSC
codes were recently updated from the year 2000 codes to the
current 2010 Mathematics Subject
Classification. These codes are organized hierarchically, first
dividing into broad research areas, then into sections and
finally into more specific research categories.
Question. How well do these codes describe the natural divisions of
research in mathematics? Could they be improved in some
way? How should they be revised?
Most of us, when submitting a research article for
publication, have to decide on the most appropriate codes
for that particular work. My own experience is that usually
there there is a natural code or two codes that fit very
well, which aptly describe the research topic of the
article. Sometimes I use two or more codes in a situation
where the work doesn't really fit well into either of them
alone, so that it isn't really a primary/secondary
classification for me, but rather a classification into the
union of two categories. Increasingly, however, I find
myself stymied by the classification scheme, frustrated in
my newest projects that perhaps four or five subcategories
are involved, with none of them truly apt, except for the
unhelpful "None of the above, but in this section"
category. In such cases, I feel that the MSC has failed
me.
I recognize that this may simply mean that I sometimes
favor offbeat topics, and so perhaps this is my problem
rather than the MSC's problem. Or perhaps my problem is
that I would like my research to be categorized by the
bottom level of the hierarchy, but I should be content just
with using the middle level of the hierarchy.
At the same time, I recognize that the mathematical
community has a specific interest in encouraging research
that crosses the boundaries between established areas,
perhaps cross-pollinating or unifying them or at least
transferring methods and techniques from one area to
another. In time, therefore, we expect subject
classification boundaries to migrate or split in various
ways. Indeed, perhaps some of the most valuable
mathematical work tends to destroy the old classification
scheme for precisely this kind of reason. Presumably, this
is part of the reason why the MSC is somewhat regularly
updated (every ten years I think).  So I suspect that there may be many people who share my frustration. 
How would you revise the MSC?
Let's have standard community-wiki rules; please provide
just one group of changes per post.

REPLY [2 votes]: First, we should ask what purpose MSC type codes serve.  After all modern papers can be indexed in full text and, even if paywalls make full text search impractical one can do a full text search on abstracts at mathscinet.  It seems to me they offer two important features.

MSC codes let one track all papers in a given are even when no particular search terms would be sufficiently specific without leaving anything out.   This allows paper archives to present their contents in a hierarchical manner or searches to be restricted to a particular subject.
MSC codes (at least in theory, I've never used them for this purpose) distinguish papers working with particular mathematical objects/approaches that can't easily be identified using keyword searches.   For instance even if I restrict my attention to papers in computability a search for "admissible set" is likely to turn up to much (admissible, like good, is overused) and miss some instances that use other terminology.

The first usage calls for a basic hierarchical description of major areas of mathematical research.  Each area should be well populated and each paper should fall into only one or at most a handful of areas.  These areas should be developed enough that they won't disappear with changes in research focus.  
The second usage calls for a plentiful list of canonical tags for particular objects, approaches or questions.  Each paper might fall under arbitrarily many such tags, the more the better.  As far as this use is concerned there is no real harm if research directions change and papers falling under some tag stop being published.  Codes should be generously added for every conceivable object/approach/question constrained only by the requirement that every such concept have a canonical code (no codes that are synonyms).  Search engines could then maintain a list of terms associated with each such code so one could do a search in computability theory for papers that mention both "model" (in the model theory sense) and admissible ordinal.
I submit that this naturally suggests two systems of codes.  One hierarchical that roughly corresponds to the first two digits + letter, e.g., 03A, of MSC2010 and the other a much more numerous database of tags and their synonyms.