Developing a 21st Century Global Library for Mathematics Research

Developing a 21st Century Global Library for Mathematics Research by Committee on Planning a Global Library of the Mathematical Sciences.

Care to guess what one of the major problems facing mathematical research might be?

Currently, there are no satisfactory indexes of many mathematical objects, including symbols and their uses, formulas, equations, theorems, and proofs, and systematically labeling them is challenging and, as of yet, unsolved. In many fields where there are more specialized objects (such as groups, rings, fields), there are community efforts to index these, but they are typically not machine-readable, reusable, or easily integrated with other tools and are often lacking editorial efforts. So, the issue is how to identify existing lists that are useful and valuable and provide some central guidance for further development and maintenance of such lists. (p. 26)

Does that surprise you?

What do you think the odds are of mathematical research slowing down enough for committees to decide on universal identifiers for all the subjects in mathematical publications?

That’s about what I thought.

I have a different solution: Why not ask mathematicians who are submitting articles for publication to identity (specify properties for) what they consider to be the important subjects in their article?

The authors have the knowledge and skill, not to mention the motivation of wanting their research to be easily found by others.

Over time I suspect that particular fields will develop standard identifications (sets of properties per subject) that mathematicians can reuse to save themselves time when publishing.

Mappings across those sets of properties will be needed but that can be the task of journals, researchers and indexers who have an interest and skill in that sort of enterprise.

As opposed to having a “boil the ocean” approach that tries to do more than any one project is capable of doing competently.

Distributed subject identification is one way to think about it. We already do it, this would be a semi-formalization of that process and writing down what each author already knows.

Thoughts?

PS: I suspect the condition recited above is true for almost any sufficiently large field of study. A set of 150 million entities sounds large only without context. In the context of of science, it is a trivial number of entities.

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