A quantum field is just a mathematical construct that models an aspect of what can happen at every point in spacetime. The fields follow rules for how they interact, and fluctuations in the fields and interactions between them, according to their respective rules, provide a good model for the universe we observe.
If you consider this purely mathematically, it’s hard to argue with. The models in question make very accurate predictions, can correctly model the vast majority of observations we know how to make, and don’t predict many things that we don’t observe. In other words, all the evidence is that it’s a very good model - a very good fit for the universe we observe.
From this perspective, one way to interpret the statement that “the universe is made of fields” is simply that the universe conforms to the quantum field model. Again, this claim is hard to argue with - it seems to me like a true statement, and there’s a lot of evidence for it.
Hawking & Mlodinow explored this in their description of what they called “model-dependent realism” - see: https://en.wikipedia.org/wiki/Model-dependent_realism
If perspectives like these don’t satisfy you, and you want to try to develop an understanding beyond mathematical models, then you have a tough problem to solve: how to go beyond the models that we know how to construct, to something that somehow gives you some sort of more fundamental insight. But what would that even look like? How would you test it? What would make this approach more true than existing theories?
In short, an answer that satisfies the criteria that you want it to satisfy may simply not be possible.
Maybe it is "made of fields", maybe it isn't, but "I think that's nonsense", which is just a gussied up way of saying "my intuition rejects that", is not a valid judgment method. The universe does not check with our intuition before doing what it Damned Well Pleases.
I assume you meant that as an obvious absurdity, but if you were going for that you probably should have avoided the concept of "language", which can be Turing Complete. Still, the main point is, whatever it is, it is, and it isn't asking us for permission to be what it is.
Some games make you better at other activities. Like, playing chess could make you better at logistics because you’re practicing planning and managing losses.
Some games match some real world situations so tightly that we can go through them step by step and solve the real world situation in the game. You can play addition to figure out two apples and two more makes four apples.
Whether the game is “real” or not is immaterial. It just needs to be internally consistent and matched to the right thing.
There’s also the idea that math is another world that we can visit, similar to the dream world. But that’s a whole other thing.
This is neat! I think it happens less in the physical world, just making up a tool and then finding its application later. It does happen in chemistry.
Magnetism isn't made of anything. It is a field, and it's one your can interact with directly.
Compare that with, say, table salt. "What's table salt made of?" Uh. It's made of atoms entirely unrelated to salt, like sodium and chlorine. "What are atoms made of?" Uh. They're made of tiny electric particles zipping around at relativistic speeds but bound together by forces like magnetism.
Richard Feynman does a better job than me of describing this exact problem in one of my favorite physics videos of all time:
The real question you raise is a very good one - how seriously should physicists take mathematical theories. If we were building a statistical model of, say, house prices and construct a reasonable linear regression model, we certainly don't believe that the market plugs the parameters of a house into the model to decide the price. The model is an approximation of the real dynamics of the market and this approximation might not hold in the future.
On the physics front, I would argue no one would consider a quadratic in speed air resistance term in Newton's second law, a fundamental feature of the universe. One can build a reasonable model that results in that term and it might even be a good approximation for some fluids in some speed/density range.
But, when it comes to more fundamental (as of today) theories like quantum electrodynamics, electroweak theory, quantum chromodynamics (all quantum field theories), or even general relativity (modulo discussions of quantum gravity) - both the predictive power and accuracy of these theories is so stunning (matching all the data generated at colliders like the LHC), that one starts wondering if we are no longer dealing with models but a true description of nature. The mathematical descriptions are also so constrained unlike the house price example above, that one can't just make modifications to the theories without violating core principles (and experimental data) like unitarity, causality, locality, Lorentz invariance etc. This only reinforces this view that perhaps this is close to a true description of what we see.
Now it is entirely possible (but IMO not probable) that this whole view will be upended and replaced by a very different physical picture. In a sense, string theory (which is now discredited heavily in the public's eye but that's a story for another day) was an attempt at a different physical picture that resulted in very rich structures that had nothing to do with physical reality.
So, physicists say that because the more time you spent understanding and studying quantum field theory and as more experiments are done (all the collisions at the LHC verify the standard model's predictions including the Higgs once its mass was known), it only reinforces that there's something deep about the current theories even though we have several unsolved problems (dark matter, dark energy, quantum gravity, fine-tuning problems).
Addendum 1: I'll add a book that is not accessible to non-physicists but gives a glimpse into the actual struggle of research and building intuition for something very abstract:
https://www.amazon.com/Feynman-Lectures-Gravitation-Richard-...
Feynman, like many others, spent considerable time applying all his powers to understand general relativity from a QFT perspective but eventually it didn't pan out (for anyone).
