I’m actually becoming optimistic that this will be solved very soon now (within two years say) . The approach that seems to be making progress is looking at the computational nitty gritty with lots and lots of computer experiments. For instance, see this and this.

Yet the thing about those two links is that the content is nearly imcomprehensible, yet you can obviously see that there is “stuff” there. I’m betting that it will be simplified and unified once the proper paradigm is discovered.