Gödel’s Incompleteness Theorem, in layperson’s language, which I phrase to myself as “there are truths which cannot be proven”: https://www.scientificamerican.com/article/what-is-godels-theorem/
(That’s not say those unprovable truths aren’t completely trivial; but it IS to say that even the best, most pure math is not automatically going to get you all the way.)
Quantum tunneling, which I see as “the universe is not just a bunch of billiard balls bouncing around in a way that would be totally predictable if we had a big enough computer”: https://en.wikipedia.org/wiki/Quantum_tunnelling#:~:text=Quantum%20tunnelling%20or%20tunneling%20(US,flow)%20appearing%20inside%20the%20barrier.
Spooky action at a distance, which I phrase to myself as “there are no limitations. How is that even possible?”: https://www.theatlantic.com/science/archive/2017/02/spooky-action-at-a-distance/516201/
«Measure photon A to be vertically polarized, and photon B instantaneously becomes horizontally polarized, even though B’s state was unspecified a moment earlier and no signal has had time to travel between them. This is the “spooky action” that Einstein was famously skeptical about in his arguments against the completeness of quantum mechanics in the 1930s and ’40s.»
Einstein is famous for saying that he does not believe that God plays dice with the universe, but I think God does exactly that. It’s just that, if the dice don’t fall the way God thinks they should, science has absolutely nothing to say about the possibility of God altering the results. (Or even about God’s existence, for that matter.)
Now faith is the assurance of things hoped for, the conviction of things not seen.
There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.
(As they say.)