You're literally arguing nothing right now. THEY took the position we should have brackets defining the order in every single equation or otherwise have them as undefined TODAY. It doesn't matter when they were invented. Obviously it's never been written like that. They are the one arguing it SHOULD BE. I said that would be stupid vs following the left to right convention already established. You're getting caught up in the semantics of the wording.

What you inferred: they're saying brackets were always around and we chose left to right to avoid bracket mess.

What I was actually saying: we chose and continue to choose to keep using the left to right convention over brackets everywhere because it would be unnecessary and make things more cluttered.

And yes, that IS a position mathematicians COULD have chosen once brackets WERE invented. They could have decided we should use them in every equation for absolute clarity of order. Saying we should not do that based on tradition alone is a bad reason.

The "always been the case" argument could justify any legacy system. We don't still use Roman numerals for arithmetic just because they were traditional. Things DO change.

Ancient Greeks and Romans strongly resisted zero as a concept, viewing it as philosophically problematic. Negative numbers were even more controversial with many mathematicians into the Renaissance calling them "fictitious" or "absurd numbers." It took centuries for these to become accepted as legitimate mathematical objects.

Before Robert Recorde introduced "=" in 1557, mathematicians wrote out "is equal to" in words. Even after its introduction, many resisted it for decades, preferring verbal descriptions or other symbols.

I could go on but if you're going to argue why something shouldn't be the case, you should argue more than "it's tradition" or "we've done fine without it so far". Because they did fine with many things in mathematics until they decided they needed to change or expand it.

Those rules are based on axioms which are used to create statements which are used within proofs. As far as I know statements are pretty common and are a foundational part of all math.

Defining math as a language though is also going to be pointless here. It's not really a yes or no thing. I'll say it is a language but sure it's arguable.

And again laws are created using statements. I have plenty of textbooks that contain "statements"

the proper way is to group it as 1+(-2)+3

No it isn't.

you can do it in any order

You can do it in any order anyway

left to right 1-2+3=-1+3=2

addition first 1+3-2=4-2=2

subtraction first -2+1+3=-1+3=2

right to left 3-2+1=1+1=2

What I meant with ““rule”” is the meme questions pray on people not understanding/remembering what the actual rules are

And you showed that you were one of them. Every answer you got other than 4 was wrong, because you didn't understand the rules. spoiler alert: doing it in different orders never means add brackets to it. Addition first for 10-1+1 is 10+1-1, not 10-(1+1). See previous textbook example

why “left to right” conventions exist

They exist because people like you make mistakes when you try to do it in a different order. Either learn how the rules work or stop spreading disinformation. Well, you should stop spreading disinformation regardless.