For nearly all of human history, we could look at the sun and the stars and find something to be calculated. From Thales predicting a solar eclipse to Newton predicting the comets and the planets to Einstein predicting the curvature of star light, we have always looked to the stars for leaps in physics.
Where the Greeks could not, Newton and Einstein arrived at axioms that nailed down reality.
As soon as we got the axioms of a new physics based on relativity, however, we also got Turing's Halting Problem and Gödel's Incompleteness Theorems. We measure thing's computational complexity and their computational irreducibility.
The recent Nobel Prizes in Physics and Chemistry, much deserved, are for aritifical neural networks and artificial neural networks for protein structure prediction, respectively. We've gotten very good at building learning machines that do well in the lack of axioms--that develop good heuristics and good approximations.
It's hard not to think of artificial neural networks as epicycles on epicycles. They are extremely useful, but in a way, dissatisfying.
There is something wonderfully soulful about the idea that Newton's and Einstein's ideas simply hung in the heavens and waited to be found. Most research nowadays seems to be predicated on the fact that that is not the case and even that that is impossible. Yet, that is also what was thought before either Newton or Einstein. No one thought to look where they did.