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?

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