Ive always thought it was interesting how much of first half of 20th was spent on understanding our limits. Relativity tells us we can't go past the speed of light. Quantum mechanics tells us that our ability to concretely talk about things goes to hell when we get on small scales. Turing showed us how weak our computers are, and Godel showed that we can't even really come up with a consistent model of logic. Lorenz showed how the nonlinear world behaved so erratically, making weather prediction hopeless. I guess thats 5 examples: 3 from math, 2 from physics. Thats all i can really think of that fits.
Thats what i think of that era in thought. Realizing we are limited. Ive read that at the turn of the century, many thought that physics as a field was dead because pretty much everything had been discovered. How cocky.