One of the problems in approaching quantum gravity is the choice for how to best represent it mathematically. Most of quantum mechanics is algebraic in nature but gravity has a geometry component which is important. (restatement)

This is similar to the early 20th century problem of how to best represent quantum mechanics: as differential equations or using group theory/Lie algebras?

This prompts the question: what other potential representations might also work?

Could it be better understood/represented using Algebraic geometry or algebraic topology as perspectives?

[handwritten notes from 2023-02-02]