I decided to remove the off topic posts going in exactly the wrong direction and this is not the place for them. FE is supposed to be easy.
Things are hard until you understand them. I tried to make a simple point but you are right it got too convoluted so I don't mind the deletion. its funny because i used to scoff about the complicated math too until things clicked not in HOW to use the math but in literally what the math is saying and acting like.
If you dig down all the way to the basics, as you say, in both math you hit "axioms" these are like the fundamental "laws" of math that are ASSUMED to be true. There is only a very small handful of axioms as they need to be as fundamental as possible and consistent as possible as they define the whole of your language aka math. Anyway very little dare to touch these axioms as they are so simple and "obviously" true. However if you keep going down and to the most ABSOLUTE fundamental axiom of nature. It comes down to a decision, and arbitrary decision. You can use all kinds of math language or better yet you can use natural language. But in essence what it comes down to is you cannot create something out of nothing
UNLESS.
And this is the "big" part that has been staring physicists and mathematicians in the face. You CAN create something out of nothing IF you create that "something" with its anti-"something". In math this is called an inversion. Or put simply in number theory. You can create as much as you want as long as you create in pairs of -1 and +1 at the time. Sure both added are 0 but you can use them separately as you please.
So how does this circle back to physics. Well modern day physics has known for ages that you can "create" matter/anti-matter pairs. In fact it happens all the time everywhere all at once in the "quantum" worlds. But this idea generalizes to everything in fact not only physics even math and beyond. To create something out of nothing you must create its inverted self.
So what is this -1/+1 pair power? In math the power of "inverse" allows you to start building an entire language around numbers and functions that map said numbers onto other numbers. And the inverse just means that if you repeat said operation that you come bacl to the original numbers. but this does not have to be a number. This means to produce ANYTHING out of NOTHING you MUST produce it as pair. A simple example is functions. For instance x2 and sqrt(2) or Sine and Cosine and so on. But then we are already in the weeds of maths so i digress. But yeah ANY language starts with a choice, a 50/50 chance choice, the choice to create a pair and arbitrary label which is the "+1" and which is the "anti" "-1" pair. A completely arbitrary and free choice, since people like free will well there it is.
Going back to reality and what we observe from quantum mechanics. It seems we can create "energy" if we can create two equal but opposite pairs and let them come close to each other. In physics this is called a particle anti particle annihilation. This "annihilation" produces energy in fact vast amounts which can be in any form you want but we can just call it "heat". So you create a pair and annihilate it and can continue to do so for essentially forever. There is no limit, this is the baffling thing about "quantum" mechanics, as long as you respect the fundamental rule of creating something with its anti pair you can annihilate it and produce energy.
Now how does one get a particle/anti-particle pair in nature. And translate that in an actually physical device anyone with a 3d printer can make without the need of a particle accelerator? Coming soon to 3d printers near you for all to enjoy.
So "math", "physics", "reality" everything is connected through the language that is being used. The beaty is its always a choice. You can dismiss a language and never get to understand it because its "hard". Or you can try and learn it to understand what is actually being said and talked about and realize that different languages seem to have the same patterns and essentially a language just allows you to interact with and observe things from a different perspective THAT is the true POWER of any language. Sure learning a new language can be hard especially in the beginning and more so with "math". But to me its not about the words or symbols used to tell a story but what we learn from the story and the NEW tools that become available to us in our OWN natural language. For example for most people its enough to only use the tools that math produces. And I am very grateful we already figured out so much already as I sure didn't want to live in the dark ages. However understanding something should imo always happen at its most fundamental level. This is true for any language you learn. This requires good teachers, people that can translate a language they understand to students that know nothing of said language and KEEP trying until ALL their students grasp at least the fundamental ideas. Anything beyond that is just bonus play time to see what else this whole system can throw at us starting from such simple basics. I am clearly no teacher let alone a "good" one. But again it all comes down to something and its anti self that come out of 0 and produce 1.
Perhaps one last example to drive this point home of how important language is. The Fibonacci sequence 0 1 1 2 3..., arguably the most famous sequence in the world. But did you know the sequence of numbers is not describing "numbers" but pairs. I didn't at least until recently, because that is not how I have seen it. But that is how Fibonacci originally formulated the problem too. You start from 0 or nothing and out comes a pair of rabbits and then you create a whole eco system. This might seem like an obvious thing as you need a male and female rabbit. But hey obvious things is what makes fundamental rules.
I honestly don't care about all the philosophical or even spiritual implications this will come with, people can believe what they want but language is everything and every language must have an inverse. If we cannot agree on what the inverse is of something then we have no language and nothing has any meaning, 'yes' becomes 'no' and things become total chaos. EVERYTHING comes in pairs at the most fundamental level and you can create as much 'pairs' as you please as long as you respect the cardinal rule that anything you create has to come with the inverse of itself. Once you have something you can create everything obviously as you now have all kinds of functions to play with or chase "theorems" to prove but that is only for those people like doing that. The rest of us can enjoy our free energy which perhaps comes with a bit more freedom too.
Let me ask a final question to anyone willing to answer it. If you were going to start a new language from ZERO. And you were free to choose any word pair to start defining, which word pair (again itself and its inverse/negation) would you chose to start with?