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This is very much a soft question, and rather a general, quite fuzzy (and perhaps nonsense and/or impossible), idea I have. I have looked around as well as I can, and mostly I found some books with traditional lists and this site.

Q.) Does anyone know if there is anything close to fitting the following description:

A graph of unsolved (possibly even some solved) problems in a specific area of mathematics (probably quite restricted), where we have names of the problems as nodes, and edges describing the relations between them.

I imagine such graphs existing perhaps for specific conjectures, and thus they would provide a good illustration of the work that needs to be done in order to solve it.

I also imagine these graphs to possibly be interactive (hyper linked perhaps), so that one could click on the nodes to get a graph of that problem and/or more information about the problem. The edges could possibly even be weighted, (and directed) to reflect the importance of that problem in relation to another.

(If not interactive then just a graph, and if not a graph, then just a detailed hyper linked database of unsolved problems, that also lists directly related problems together with their importance to that specific problem, but this is of course already close to wikipedia's pages.)

The restriction mentioned in §1 under Q is of course just there for convenience. In a sense, the more problems such a graph would incorporate the better, however this puts a lot of requirements on the functionality of the graph, for it to be useful. Perhaps we could imagine a graph where only the most important problems (graded according to some rules) are visible at a single time. Clicking on a problem could open up a similar graph of that problem and so on.

EDIT: I actually found this thread now, via the 'related' list. I did not see this there while I was writing the question. This thread of course touches on several questions related to this one.

  • What are the edges of such a graph supposed to indicate? – John Bentin Mar 15 '17 at 18:13
  • So what you're essentially asking for is essentially like the course-map from ocw.mit.edu but for solved and open problems in mathematics. I imagine that to be quite a formidable task, for it would probably be a very large graph/map. – Nox Mar 15 '17 at 18:19
  • @JohnBentin: Possibly a relation between problems P1 and P2 (of some sort), say that the truth of P2 implies something that can be used to show P1, this could perhaps indicated by a directed arrow P2->P1. But since there could be many such connections, this could be built up like a graph. This is all very fuzzy, I agree, and I am not very experienced in researching mathematics and/or proof theory. – Christopher.L Mar 15 '17 at 18:20
  • @Nox: Yes, I agree, so it would probably be a better idea, as I mention, to restrict one self to perhaps a singe conjecture of certain interest or so. I was just curious to see if anyone knew of anything like this existing. But of course, the next best thing (better in some aspects) would be to have a hyper linked database, but with the additional listings of related theorems/conjectures. And is wikipedia the closest thing to that we have? – Christopher.L Mar 15 '17 at 18:26

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