Is there a body of research of "theory"? I feel like the state-of-the-art algorithms represent incremental improvement moreso than an implementation of state-o

Is there a body of research of "theory"? I feel like the state-of-the-art algorithms represent incremental improvement moreso than an implementation of state-of-the-art theory. Kind of like Donald Knuth's dancing links, these improvements seem to come from "aha!" type exploration moreso than building upon a theory. Maybe that's typical? As a metaphor, it feels like with algorithms we are still Newton observing apples whereas there could be an entire Newtonian physics (of algorithms) out there. Some logic that underlies the field. My understanding is that the abstract goal of any lookup algorithm is to map a series of bytes to an index such that the item at the indexed position can be dereferenced. The concept of hashing being to convert an arbitrary data type (string, integer, etc) to a sized integer. By abstracting the integer away to it's bytes, we have the above problem statement to solve. Other than that base understanding, I don't know what to research next in the field.