Part of why math is effective is that its extraordinarily compressible. And you can take those ideas and apply them elsewhere (composition works well). The natural world has a lot of detail and is therefore hard to compress. That's why it's a good source of new ideas. Consider the relation between the McCulloch–Pitts neuron (MCP lol)[2], developed to model biological spiking neural networks, and an inspiration for modern artificial neural networks.
[1] https://arxiv.org/abs/math/9404236 [2] https://en.wikipedia.org/wiki/Artificial_neuron
Interesting. My intuition here is quite the opposite, that math is vastly overpowered for physics. I don't think we invest a lot of work in figuring out math that isn't useful to describe the natural world.
The best counterexample I could come up with was lasers. Yeah, all the pieces are there in quantum mechanics, but so far as I know, nothing in nature lases.
Semiconductor chips. Again, yes, all the physics is there, but you're going to be reaching pretty far to find something in nature that's like a CPU chip.
Dyson spheres.
Interrupt vector tables.
Riemannian geometry.
Databases.
I'm sure that people can poke holes in some of these (with varying degrees of far-fetchedness as to how directly the same concept is in nature). But I think there are enough counterexamples, where nature's "prior art" is indirect enough, to make the absolute version of the statement false.
"Humans rarely discover something that doesn't already exist somewhere in nature"? Yeah, that's probably true.
https://en.wikipedia.org/wiki/Rotating_locomotion_in_living_...
And yet, whoever invented the wheel and axle, I'm pretty sure they didn't do so based on the bacterium's flagellum.
So, yes, the concept existed in nature. But it wasn't the inspiration for the human invention in any way.
I think there's a provocative human-intelligence analog to be found there: "humans will never discover anything that doesn't already exist somewhere in nature. We can only recombine concepts we've seen—never invent truly new ones".
It's said that mathematics is "unreasonably effective" at describing the natural world. But what about the other way around? What if mathematics is unreasonably ineffective at escaping the convex-hull of concepts and patterns found in nature?