I don't have any particular recipe [for developing new proofs] ... It is the reason why doing research is challenging as well as attractive. It's like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.
The study of topological phases of matter is not just about discovering new materials; it's about uncovering the fundamental principles that govern the quantum world.