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.
Best Answer
I would add a top-level subject code roughly corresponding to the arXiv math.QA. Currently my field (quantum groups, knot invariants, TQFT, monoidal categories, etc.) is listed under 16T, 17B, 20G42, 58B32, 81R50, 57R56, 81T, 57M, 56L37, and 18D. But there's no top-level classification that's appropriate, I end up having to describe myself as 17 "Nonassociative rings and algebras" which is terribly misleading. Math.QA is perfect, and the MSC just doesn't have anything like it.