> There are several hard problems in one domain that are trivial in another domain, for example. Certainly, and this is pretty much what OP did, invent a new d

> There are several hard problems in one domain that are trivial in another domain, for example. Certainly, and this is pretty much what OP did, invent a new domain to solve a problem – Hamilton aka Lord Kelvin merely reformulated the problem slightly, and while I personally love Hamiltonian mechanics, I don’t think it is comparable to ‘inter-universal geometry’ or replacing first order logic with something else. So, yes, a different field may provide a different perspective and hence easier solution, but if you want to replace first order logic, you’re not looking at a different/new field in maths, you’re looking at rebuilding maths.