It will be quite challenging to address approach (2) above as some mathematical proofs include a number of gaps and, thus, are really hard to formalized. Some mathematicians are neither willing nor do they seem to have the ability (yet) to encode their knowledge in a way that it can be easily converted into machine-readable formats.

If we require professional mathematicians to fill all gaps, we will hamper digitalization of mathematics. Ideally, tools for professional mathematicians would allow them to include gaps and talk on very abstract level. But where is the border of granularity these tools would need? How many gaps can you allow and what background knowledge needs to be provided?

If we allow professional mathematicians to digitalized proofs with gaps, this mathematical knowledge will not be accessible to all users, thus contradicting with the vision of mathematical knowledge management, which aims at making mathematics accessible to all. Instead, we would require users to have some basic mathematical understanding. This sounds reasonable on a first glimpse, but where do we draw the line? Do we expect that all users have elementary school,secondary/ high school or university education?

Without respective tools (e.g. formulae editor), scientists are not encourage to digitalize their mathematical thoughts directly. However, some tools provide intuitive interfaces and languages (in particular for logicians, maybe not for all mathematicians in general): Functional languages (such as ML, HASKELL, Scala) provide very intuitive ways of writing mathematics (currying, uncurrying): They are very close to the formal mathematical language and provide type inferences and therefore type soundness. These languages illustrate that it is possible to design a syntax that allows to model mathematical structures; basically allowing to write mathematics with very little system-dependent adaptations (Normen illustrated several examples).

Regarding the trust in computers, some users of system such as Mathematica and Maple seem have full trust (“blindes Vertrauen”) in the systems and their type inferences.

Normen pointed to Plato, developed by Marc Wagner, Omega Group, University of Saarbrücken, Germany. Plato provides an intuitive interface (LaTeX-based syntax for mathematical notations, mark-up of other document fragments such as definitions, proofs) and is integrated with the Omega system, which it used to automatically evaluate/ verify the mathematical parts of the documents.

Normen also mentioned work that we have seen at the MKM: An approach that allows to digitalize mathematics on a very abstract level and that uses heuristics and tactics to break down these abstract statements into a machine-readable form.