SkyeStarfall

Quick question, are you disabled yourself?

Wich turned it basically into an US exclusive product, and pretty much impossible to get outside of there

Maths is so much more malleable and abstract than what you think it is. You really do not understand maths as well as you think you do, and I feel a bit sad for any student of yours that would wish to explore some deeper revelations of maths, just to be told "nope! That's just how it is!" with no further thinking at all.

A lot of maths is chosen. Choices with good motivation, but choices nonetheless. So long as there not being contradictions or paradoxes, the formulation of a form of math is valid. Which is why you have different forms of maths with different rules.

And you really could use some more humility, it's obnoxious when you act all so high and mighty and arrogant, with no interest in questioning your assumptions. Devolving into ridiculing the person you're discussing with and a general vibe of "omfg I'm right you fucking idiot because I'm right how dumb can you get??"

Like, what is it that you want here, a book from the 700s of the one dude that invented arithmetics and told clearly "I chose this."? You are making your arguments effectively unfalsifiable by just going "Nuh uh" all the time.

Get some humility and learn a bit about the foundations of maths. Like. Down to set theory. See for yourself what actually is the foundation. And, spoiler, it's not a high school textbook. Hopefully I do not need to tell you how concepts are simplified for younger students, instead of overwhelming them with the complete knowledge of a subject.

I mean, it is pretty clear here that you do not really understand the purpose of notation, nor what maths is. Notation is just a constructed language to convey a mathematical idea, it's malleable

And yeah, it's easy to just say "this page is wrong!" without any further argument. Nothing you referenced proved the convention as law, and neither is there any mathematical basis for any proof, because it simply is nonsensical to "prove" a notation. Have another source for this being convention https://www.themathdoctors.org/order-of-operations-why/ or https://math.stackexchange.com/questions/884765/mathematical-proof-for-order-of-operations. If you want a book about this, then there's https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev that is cited by wikipedia. I'm sure you could also find stuff about this in a set theory book. Though good luck understanding them without sufficient experience in high-level maths

Really though, maths is so much more than "3+5=8 because that's the correct answer!" But why is it the correct answer? In what context? What is the definition of addition? How can you prove that 1+1=2 from fundamental axioms? This is harder to answer than you might think.

That's a very simplistic view of maths. It's convention https://en.wikipedia.org/wiki/Order_of_operations

Just because a definition of an operator contains another operator, does not require that operator to take precedence. As you pointed out, 2+3*4 could just as well be calculated to 5*4 and thus 20. There's no mathematical contradiction there. Nothing broke. You just get a different answer. This is all perfectly in line with how maths work.

You can think of operators as functions, in that case, you could rewrite 2+3*4 as add(2, mult(3, 4)), for typical convention. But it could just as well be mult(add(2, 3), 4), where addition takes precedence. Or, similarly, for 2*3+4, as add(mult(2, 3), 4) for typical convention, or mult(2, add(3, 4)), where addition takes precedence. And I hope you see how, in here, everything seems to work just fine, it just depends on how you rearrange things. This sort of functional breakdown of operators is much closer to mathematical reality, and our operators is just convention, to make it easier to read.

Something in between would be requiring parentheses around every operator, to enforce order. Such as (2+(3*4)) or ((2+3)*4)

The rules are socially agreed upon. They are not a mathematical truth. There is nothing about the order of multiple different operators in the definition of the operators themselves. An operator is simply just a function or mapping, and you can order those however you like. All that matters is just what calculation it is that you're after

We have discovered over 6000 exoplanets in total, and over 100 in this year. I'd be surprised if you knew of all of them

I mean, arithmetic order is just convention, not a mathematical truth. But that convention works in the way we know, yes, because that's what's.. well.. convention