Math is the programming language of the universe and physics is the rule book.
Some of those rules can be bent. Others can be broken.
Wait... Kung Fu is just maths for Asians?
That’s a good way to put it.
I’d personally amend it to this though:
Math is the language we use to write pseudo-code for the rules of the universe. It allows us to reasonably predict and share/write our understanding of the universe.
The best algorithms then match with the actual universe even if the real thing doesn’t use the math (looking at you -1, infinite points and black holes)
the cool theory you don’t understand is very likely also math
I would argue that physics is based more on experiments than math.
Physics is basically "some guy way cooler and way nerdier than you 100 years ago did some experiments observing this law, and because of that we can use really hard math to predict the whole universe."
Some very specific experiments, precise and weird enough to produce some truly abstract results with strong hints of things like electron spin, neutron decay via the Weak Force, photon entanglement.
Or out in the field - imagine hiking to the top of Ben Nevis in Scotland, then going up a further couple of kilometers on a balloon, carrying a camera and a vacuum chamber with an alcohol gas cloud within, to photograph the trajectories and interactions of mysterious particles from space.
Back at Edinburgh or Manchester, wearing your tuxedo on weeknights, for an evening of drinks at the gentlemen's club, discussing the latest results and implications with your peers, over single malts and cigars.
You're not wrong, but we're doing the experiments to test the theory, and that requires some math
Or: We're using math to summarise what the experiments have said so far. And then using that to extrapolate what might happen in the next experiment.
Thats how it used to be. Now physics is eating its own theoretical tail.
Plenty of physics sub-fields are still led by experiments, such as condensed matter physics. I don't know if your statement applies to anything other than particle physics?
Physics is just applied math and math is just abstract physics without universal constraints.
They are two sides of the same coin that is universal logic, which views fundimental abstract concepts and the arrangement/ change of physical structures as equally important in its operations.
Maybe the distinction between prime number and boson breaks down at some level of reality as pure information packaged in slightly different ways. The same laws that govern the fractal dance between order and entropy build similar geometries whether working with imaginary numbers in the complex plane or arranging base atoms into higher orders of being within in the observable universe.
Thanks to Gödel's incompleteness theorem at least we know we will never really have a complete picture of the truth of it.
How relevant is this to modern Physics?
As far as I know, modern math is mostly dealing with set theory and some imaginary 17D pringles in empty space, while modern physics is dealing with some imaginary 17D pringles in... uh...
Well, to put it this way, if decent writing is a prerequisite for doing math, does that mean that all math is essentially just applied poetry?
What do you mean by modern physics, exactly?
In general, even simple problems can get very messy very fast without simplifying the scenario.
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