I have the feeling that the challenge of bringing mathematicians and computers closer together, requires a lot of expertise in the field of pure mathematics and the more technical-field of mathematical knowledge management. The latter requires a good overview on mathematical tools, in particular, computer algebra systems and theorem provers as well as other mathematical editors (e.g. Plato). Moreover, the step-wise formalization of mathematical text seems to be a core interest and competence of the whole KWARC group rather then my own research focus.
Looking at the discussion with Cris on the confidence in proofs, acceptance of proofs as well as trust in proofs, I am wondering, whether we could use our understanding of the mathematical practice and use it for providing an assessment and reputation system for mathematics, i.e. something that we could attach onto a repository of mathematical knowledge and use to facilitate the collaboratively assessment of the mathematical community on different layers:
- Is (the proof) published in journals (considering the impact factor of these journals)
- Was it accepted by the Zentralblatt or Mathematical Reviews (adding more confidence)?
- How long was the proof tested by the mathematical community?
- How many proofs do exist for the theorem?
- Is it a nice proof/ theorem (beauty)?
- Is it correct? (later adding automatic verification methods …)
- Can it be understood (e.g. measured by the numbers of references and re-uses)? How hard can it be understood?
- Is it re-used by the community, i.e. is it relevant and useful for further mathematical work?
We can imagine a top-down and bottom-up approach:
- The top down approach requires the user’s explicit assessment of the content: evaluating the users’ ratings, tags, bookmarks
- The bottom up approach could implicitly provide the relevance of content making use of the logical and narrative structure of the mathematical knowledge: computing theory interrelations, citations, …
I will discuss with Cris, whether he thinks that this would lead to a useful application for mathematicians.
[...] An assessment system for mathematical knowledge: Cris said that my proposal is still to vague and abstract to be understood by other scientists. He made an example to illustrate that I should work on my presentation of new ideas (freely cited, not his actual words): “When I present my view to solve a mathematical problem I need to include to things: (1) I need to provide a number of concrete steps towards the solution, i.e. first I proof this, then I proof this, … and I have to point to the basic methods I will be using, e.g. I’ll use graph theory rather then topology. (2) I need to point to my previous accomplishments, i.e. some steps I have already addressed. Then people will accept it more likely.” Cris also said, that for the existing achievements, I do not necessarily have to provide my own work, but I can point to existing research and that will increase my acceptance. So what I will do for my seminar talk is, to put more emphasis on the methods and related work part. And I will use many examples to illustrate my approach. I will have a look at Cris GoogleTalk again. [...]