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For reference, the poorly named "standard model" which is the quantum theory of all forces except gravity, cannot really be called equations in the usual sense. This is because the kind of mathematical model that would describe the standard model (nonperturbative QFT) can't currently be done rigorously. It can only be done for simpler models in lower dimensions. The standard model is a very complex sort of approximation to a theory that is assumed to exist.

This might be a mere detail to some but to me it is a sign that physics is complex in all kinds of ways, and can't really be described as "choosing the right equations". Even if you think that this is what physics is fundamentally, I think you would have to admit that it wasn't possible to describe what the meaning of "equation" was before qft was developed, and the same may be true about future theories that unify the standard model and gravity.

I don't think this really addresses my objections. The fact that physics is described mathematically could be an artefact of how mathematics is the most "agreeable" way for humans to come to a consensus. It seems to me inescapable that mathematics is inherently anthropocentric.

I think this is a false dichotomy:

> ...either everything in physics will always be rooted in math, or else some "non-math stuff" has to be discovered.

I can imagine a plethora of other possibilities. For example, there may be nothing "at the root " of reality, no ultimate equations. We might get better and better at predicting and manipulating the universe around us, but never close down on some ultimate truth.

> For one thing, what has physics ever come up with but equations, and improved equations to replace those, and so on?

Observations of nature and rational explanation of those in terms of old but also new concepts. Equations are just one of technical artifacts to help us think in a precise way. If we had computers sooner, there might have been physics without differential equations.

What observations are made in physics experiments which don't end up expressed as a cluster of floating-point numbers?

I think the previous comment was getting at concepts like "the laws of physics are the same in all inertial reference frames". It doesn't directly refer to any mathematics, although of course it can only be tested via the quantitative predictions that follow from it.

I understand the statement "the laws of physics are the same in all inertial reference frames" as referring to correspondences and invariances among some math under a coordinate transformation.

I think you're missing my point. Physics did not give us merely equations, it is also gave us concepts such as force, temperature, energy and physical principles such as principle of conservation of energy, principle of relativity etc. (Floating-point number is a concept referring to implementation of rational numbers in computer engineering. I do not think it is relevant here.)