Of course there are many different notations. One need only look to Newton and Leibniz notations for calculus, or Schrodinger's wave equations and Heisenberg's matrices for quantum mechanics, to know there's a long history of different mathematical abstractions for the same concept.
In my own field, I recently discovered (by reading the literature and getting feedback from conferences) that there appears to be a previously unknown connection between this maximum common subgraph problem and frequent subgraph mining, so it's not like connections are altogether rare.
Indeed, I'll argue that these occur all the time, and research libraries exist in part in order to help people find them.
Which is why I asked why this project might be better than traditional means, and I gave an real-world example to give a basis for discussion.
[1] There's plenty of MCS research, but since the problem itself is known to be NP-hard, most of the mathematical work shows that certain limit cases, like planar graphs or outerplanar graphs, is solvable in polynomial time. As the structures I deal with don't all fall into those categories, I can't use them as a general purpose solution. [2]
[2] I might be able to use them as a special purpose solution, and this project might help identify codes I can use for this case. I just can't figure out a way to make it easier than the current methods.
Why would anyone write about not finding a shared abstraction? You have a significant publication bias there.
Lots of domains share the same mathematical abstractions, but we don't know because (almost) nobody is trying to discover them. We can know that it's common, because once in a while people do look, and always come back with new shared abstractions.
If somebody created an index that took different notations into account, that'd revolutionize research. But I don't think this system does that.