YouTube Comment on Calcea Johnson and Ne’Kiya Jackson’s Discovery, and How All Modes of Mathematics are Proven

Pythagorean Theorem is one of the most proven concepts in mathematics, and for the calculus to reason to it, proves the Calculus works. So also, the calculus is a proof in itself, being so founded in empirical knowledge, that the Pythagorean Theorem works. It's proving itself empirically. Just like the kindergarten proof we use with the apples, for addition and subtraction.

Calculus is an empirical method. Just like you can prove Quadratic Equations, by simply using it to do rudimentary cuts. So also Geometry. It's a different form of proof... more useful in many ways. But that's how Euclid proved his Theorems in Elements. It wasn't with algebra, but with a compass and ruler and piece of string.

As a basis, we know the Calculus and Algebra work. But, the fact that this method turns into the Pythagorean Theorem, is in itself a proof of Pythagorean Theorem, because Calculus is an empirical science, and is simply explaining the axiom of a Right Triangle. As it should. If it didn't, we'd have to question whether the method worked.

 In logic it's called a biconditional. And they would prove themselves by both being tautologies.

It's also premised on the notion of Equalities in Algebra and Calculus. Really the fundamental aspect of all mathematics. And since the Logic of Calculus explains the axiom of Pythagorean Theorem, we know the Calculus works, too.

At the base of the issue, it's proven through observation. Both. Calculus is one of the most proven things in history, and so is Pythagorean Theorem. It only makes sense that they'd both compliment each other.

Rooted in the empirical observations of both, and how each is so well proven, they both contiguously prove the other.

If their proof were purely deductive, it would be circular, but it's empirical. It's a posteriori and not a priori, therefore, it cannot be circular. The empirical fact is rooted in the Calculus observing the axiom of Pythagorean Theorem, which is proven over three hundred times. So it is itself trustworthy. So also, the axiom of Pythagorean Theorem is proven, by the fact that Calculus is an empirically proven method, used in all forms of mathematics, without which, no engineering could flourish.

 It should be standard at every college math program in the STEM field. It's an important concept that I'm trying to tease out of it. It is philosophy, so to speak, but one needs philosophy to truly understand mathematics. 

Just the sheer saliency of the proof, in that it must work. That's something the world sorely needs in modern day. One can apply the same reasoning to literature, and get true ideas, too. As we kind of are hitting a brick wall, because nobody understands math empirically. They understand it deductively, and that's why so many people are lost in the weeds, and are trying to reinvent algebra or number systems.

It uses calculus to define the parameterisations. It is an elegant proof of all mathematical concepts, at once. At least, I'll make sure it's understood that way.