In many European countries, e.g. Germany, there is a strong movement that all research data should be freely available according to the FAIR principles (findable, accessible, interoperable and reusable). See https://libereurope.eu/wp-content/uploads/2017/12/LIBER-FAIR-Data.pdf

This is a major challenge for scientists who produce massive data, e.g. from numerical simulations, but also for mathematical research as a whole.

How and in which form can we standardize the way to find mathematical formulas or mathematical theorems, when different communities use different terminology for the same objects while the same formulas for different objects?

The German Science foundation DFG has just started a large call for building research data infrastructures to deal with this, see e.g.

https://www.dfg.de/en/service/press/press_releases/2018/press_release_no_58/index.html

Most people in the mathematical community seem to ignore these developments, but this may lead to real threats for the community if we do not join the movement right from the beginning.

Examples of such threats could be that standards will be fixed that are incompatible with our current way to produce mathematical articles (in LATEX) and PDF or that the way formulas are stored is just graphically. Another problem may be that standards for model generation, mathematical software, or simulation data are not as we like them. It is clear that commercial code providers are heavily lobbying with governments to make standards that are good for them and that IT companies and data analytics people have their own views of how data should be adressed.

The mathematical community must unite in a common quest to be on board right away in the developments (the German math community has already decided to do this and is participating in a joint consortium proposal) and to make these principles realistic for mathematics and the neighbouring sciences and to preserve and improve established publishing standards to be able to deal with future developments. This may require also the construction of new and uniform concepts, such as semantic annotation of formulas or theorems.