Thomas Fischer: Position Statement

For the successful build of a World Digital Mathematics Library, some infrastructure is necessary. This refers to some sort of "meta-structure" beyond the collection and curation of digital versions of mathematical texts. The following are some suggestions for this building blocks for this structure.

1. Multilingual mathematical dictionary and/or thesaurus
   The majority of historical mathematical texts in the western world appear to be in English, French, German, Italian, Latin and Russian. There are also texts in Czech, Hungarian, Polish, Portuguese, Spanish, Swedish and other European languages.
   It would be extremely helpful for research in this body of text if a multilingual mathematical dictionary would be availably to search for words simultaneously in those different languages, taking into account the special use of everyday words in mathematics.
   In addition, any support in the translation of these texts (restricted to the language, omitting formulas) would be very welcome.
   Furthermore, there is a vast amount of historical mathematical literature in non-European languages, e.g. Arabic, Chinese and Indian languages, Japanese. If at all feasible, the dictionary and translation tools should be extended to those languages as well.
2. Extension of classification (MSC), keywords and possibly reviews to historical texts
   Standard references in mathematics are MathSciNet and ZMATH. Unfortunately, they do not cover historical literature, and classification according to the Mathematical Subject Classification (MSC) is not generally provided for papers before the creation of the MSC (1991). A serious effort to alleviate those shortcomings was the Electronic Research Archive for Mathematics (ERAM) or "Jahrbuch" project, but this could only provide first steps in this direction.
   Thus important information for structuring collections of mathematical literature is missing. To provide this structure, an extension to older mathematical texts is desirable.
   In addition, for MathSciNet and ZMATH (and probably other review journals) to become central hubs for the WDML, alternative funding models would be needed for these journals. It is hard to imagine how a WDML could be created without references to these journals.
3. Mathematical Name Authority Files
   While the MSC can serve as subject authority files, it would be useful to have specialised Name Authority Files for mathematicians or a defined section of standard authority files tagged as "mathematics". This could reliably disambiguate persons with identical names (Fischer?) and merge entries with different versions of the same name (think Tschebyschew…). In addition, a register of mathematical (or earlier academic) journals would help to structure the collection.
4. Universal citation resolver
   A service that would take references to mathematical sources in the form that they occur in mathematical texts (possibly with a reference to the journal or the year the citation stems from) and returns a unified and enriched version of the reference, with a reference to the digital version if available.

The question of scope of the mathematical library should be taken on rather broadmindedly. Beyond the incorporation of the mathematical works considered by those review journals, the integration of "grey texts" is desirable. Not formally or widely published texts may contain important contributions to the mathematical knowledge. This would include in particular (electronic) theses and dissertations as well as papers deposited in pre- or postprint repositories.
It also would be time misspent to try to differentiate in (early) academic journals between mathematically relevant texts and those referring to natural sciences.