An Auto-Generated Cartography of Mathematical Theories: Has it been done already? While looking for a way to visualize the logical structure of mathematical theories a graph-like depiction came to my mind, where propositions are represented by vertices.  An edge goes from proposition A to proposition B if A has been used in the proof for B.  I know there are formal systems which represent mathematical knowledge and proof, so it should even be possible to automatically generate such a graph.  Has something like this been done already?
 A: There's certainly nothing perfect yet, but I know of two things that are somewhat close to what you describe.
Firstly, paperscape has a big visualization showing all the papers on arXiv, and you can see important recent papers and get a vague sense for which papers are connected to which other papers. It doesn't show propositions, and by necessity the papers are essentially all about relatively recent proofs, but it's something.

I know there are formal systems which represent mathematical knowledge and proof, so it should even be possible to automatically generate such a graph.

This has been done, but there are severe limitations on the meaning of such a graph. Firstly, any particular system will usually only have one proof of a given theorem, when certainly theorems can be proved in different ways. Secondly, any system has only a fairly small amount of things formalized, so that it wouldn't be close to representative of math as a whole. Thirdly, though this may not be a problem for all systems, most proofs will use common low level facts like modus ponens, so that an aesthetically good picture would require manually removing such facts from consideration.
With these caveats in mind, you can see the state of the metamath proof explorer in this Google Groups post by Mattia Morgavi. If you scroll down a bit, you can see a striking labeled amoeba-like graph based on removing the low-level facts.

If you prefer Twitter to Google Groups, both of the above are on display in this tweet.
