SmartmanApps

That's cool. I'm not sure what you mean about not using it as a source though, because that was also my point! If you want sources for how this should actually be done (and what actually is taught at school), then see my thread - contains actual textbook references (where there's a screenshot of a textbook, the place it's come from is in the top-left of the screenshot), actual historical documents (Lennes and Cajori), worked examples, proofs, etc. You said you believe in "strong juxtaposition", so we're kinda in agreement - I'm just pointing out that the actual rules are Terms and The Distributive Law (i.e. 2 different rules have been lumped together as one under the "strong juxtaposition" banner), neither of which is discussed anywhere in the blog (and when I, and others, have pointed this out, the OP has ignored us and downvoted our comments). I also made 5 fact check posts rebutting the false/misleading claims made in the blog - just sort the comments here by "new" and you'll see them (no prizes for guessing who downvoted them).

In other words, I wasn't saying "don't pay attention to any blog posts" (which I think is what you thought I meant?), I was saying "don't pay attention to this blog post" (for multiple reasons that I've posted in many places in here).

Not sure how you came up with that conclusion. I never said anything about it being "just a blog post".

You said...

I don’t understand how the author of the post lands on “there is no good or bad way, they are all valid”

And I'm pointing out he arrived at that by ignoring what's taught in high school, which is where it's taught (not in academia). It's like saying "It's ambiguous if there's such a thing as rain" if you present weather evidence which has omitted every single rainy day that has happened. i.e. cherry-picking. Every single blog which says it's ambiguous has done the exact same thing. You can find what actually is taught in high school here

Check a high school Maths textbook - even easier!

It's what is actually taught in high school, so there are those who remember and those who don't.

You are correct with your definition - Terms are separated by operators and joined by grouping symbols - and it's consequently not ambiguous at all (using so-called "weak juxtaposition" breaks that rule).

enforce writing math without ambiguity

It already is written without ambiguity.

were taught in third grade

This is actually taught in Year 7 - the people who only remember the 3rd Grade version of the rules are the ones getting it wrong.

There isn't ambiguity to begin with - just people who have forgotten the rules of Maths.

I wanted to compile a list of points that show as clear as humanity possible that there is no consensus here, even amongst experts

And I wrote a bunch of fact checks pointing out there is consensus amongst the actual experts - high school Maths teachers and textbook authors, the 2 groups who you completely ignored in your blog post.

What’s especially wild to me is that even the position of “it’s ambiguous” gets almost as much pushback as trying to argue that one of them is universally correct.

That's because following the rules of Maths is universally correct.

arguing vehemently that implicit multiplication having precedence was correct and to do otherwise was wrong, full stop

He was using the wrong words, but he was correct - the actual rules are The Distributive Law and Terms ("implicit multiplication" is a rule made up by those who have forgotten these 2 rules).

Yes, unfortunately there are some bad teachers around. I vividly remember the one I had in Year 10, who literally didn't care if we did well or not. I got sick for an extended period that year, and got a tutor - my Maths improved when I had the tutor (someone who actually helped me to learn the material)!

why that’s actually ambiguous.

It isn't actually ambiguous. You have remembered what you were taught in school, unlike the author of the blog post, who manages to write the whole thing without ever once checking a Maths textbook (which would reveal the only correct answer to be 1).

It treats division like a fraction

Which is why it gives the wrong answer.

Also you shouldn't be adding a dot between the 2 and the brackets - that also changes the answer.