It took me nearly a decade of working in distributed systems to be introduced to TLA+ and other tools in this space. Until then my knowledge had been built from textbooks describing the fundamental data structures, algorithms, and protocols... but those texts take an informal approach with the mathematics involved. And since I was self-taught I was reading those texts with an eye for practical applications than for theoretical understanding. I had no idea that a tool existed that would let me specify a design or find potential flaws in systems and protocols, especially concurrent or parallel systems, with such ease.
I think type theory and category theory have also been great tools to have... but I think mathematics in general is probably the more useful tool. Being able to think abstractly about systems in a rigorous way has been the single-biggest booster for me as a practitioner.