A big part of what’s impressive about Noether’s theorem is that it’s not at all mysterious. At its core, it’s a mathematical proof that’s possible to fully understand. It doesn’t depend on any magic constants in our universe, or indeed anything in the universe at all. It should apply to all possible universes in any situation that satisfies its conditions. The PLA is similar.

Some people see a mystery at the point where these mathematical constructs are applied to our physical universe. Eugene Wigner wrote about “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”

There are explanations for many of the points he raised in that paper. Perhaps the one that remains most unresolved is the question of why universal law or behavior isn’t messier, more chaotic - why it should so often correspond so neatly to physical phenomena. Intuitively, this doesn’t seem surprising to me, but Wigner correctly points out that we don’t really know why this is the case.

Answering that gets deeper into philosophy: structural realism, the anthropic principle, and so on. But one possible explanation is an extension of ideas like Noether’s: that the various mathematical constraints collapse the space of possibilities enough to make it likely, if not inevitable, that the universe ends up embodying relatively simple mathematical structures.