The ambiguous ones at least have some discussion around it. The ones I've seen thenxouple times I had the misfortune of seeing them on Facebook were just straight up basic order of operations questions. They weren't ambiguous, they were about a 4th grade math level, and all thenpeople from my high-school that complain that school never taught them anything were completely failing to get it.

I'm talking like 4+1x2 and a bunch of people were saying it was 10.

I found a few typos. In the 2nd paragraph under the section "strong feelings", you use "than" when it should be "then". More importantly, when talking about distributive properties, you say x(x+z)=xy+xz. I believe you meant x(y+z)=xy+xz.

Otherwise, I enjoyed that read. I'm embarrassed to say that I did think pemdas meant multiplication came before division, however I'm proud to say that I've unconsciously known that it's important to avoid the ambiguity by putting parentheses everywhere for example when I make formulas in spreadsheets. Which by the way, spreadsheets generally allow multiplication by juxtaposition.

I just finished your article and wow! I'm definitely going to save it and share it the next time I come across another one of those viral problems. It was incredibly thorough and well researched, you clearly put a lot of energy and effort into it and it blew me away. It was really refreshing to see someone articulate themselves so passionately with supporting research. I look forward to reading more of your work!! 👏

A couple of edits (not trying to be rude but people sent to your article are going to be pedantic)

*current beliefs

This sentence needs editing: "They even split the category into two and the make a distinction between implicit multiplication with variables other implicit multiplications."

It’s also clearly not a bug as some people suggest. Bugs are – by definition – unintended behavior.

There are plenty of bugs that are well documented. I can't tell you the number of times that I've seen someone do something wrong, that they think is 100% right, and "carefully" document it. Then someone finds an edge case and points out the defined behavior has a bug, because the human forgot to account for something.

The other thing I'd point out that I didn't see in your blog is that I've seen many many people say they need to evaluate the 2(3) portion first because "parenthesis". No matter how many times I explain that this is a notation for multiplication, they try to claim it doesn't matter because parenthesis. screams into the void

The fact of the matter is that any competent person that has to write out one of these equations will do so in a way that leaves no ambiguity. These viral math posts are just designed to insert ambiguity where it shouldn't be, and prey on people who can't remember middle school math.

Don't forget math with fruits! https://imgur.com/JOuRhQ3

The order of operations is not part of a holy text that must be blindly followed. If these numbers had units and we knew what quantity we were trying to solve for, there would be no argument whatsoever about what to do. This is a question that never comes up in physics because you can use dimensional analysis to check to see if you did the algebra correctly. Context matters.

I feel like if a blog post presents 2 options and labels one as the "scientific" one... And it is a deserved Label. Then there is probably a easy case to be made that we should teach children how to understand scientific papers and solve the equation in it themselves.

Honestly I feel like it reads better too but that is just me

A fair criticism. Though I think the hating on PEDMAS (or BODMAS as I was taught) is pretty harsh, as it very much does represent parts of the standard of reading mathematical notation when taught correctly. At least I personally was taught its true form was a vertical format:

B

O

DM

AS

I'd also say it's problematic to rely on calculators to implement or demonstrate standards, they do have their own issues.

But overall, hey, it's cool. The world needs more passionate criticisms of ambiguous communication turning into a massive interpration A vs interpretation B argument rather than admitting "maybe it's just ambiguous".

I don't see the problem actually.

1. Everything between ()
2. Exponents
3. multiply and devision
4. plus and minus
5. Always work from left to right.

==========

1. 1+2= 3

2. No exponents

3. • 6 devised by 2 (whether a fraction or not) is 3
   • 3 times 3 is 9

4. Nothing remains

I agree with your core message, that the issue is caused by bad notation. However I don't really see why you consider implicit multiplication to be the sole reason. In my mind, a/bc is equally as ambiguous as a/b*c. The symbols are not important.

You don't even consider this in your article, instead you seem to take the position that the operations are resolved from left to right. This idea probably comes from programming languages, as they commonly use this convention, but I haven't seen this defined in mathematics anywhere. I'm open to being wrong here, so if you can show me such a definition from an authoritative source (maybe ISO) I'd be thankful.

As it stands, you basically claim "the original notation is ambiguous, but with explicit × the answer is obviously nine, because my two calculators agree", even though you just discounted calculator proofs. By the way, both calculators explicitly define this left-to-right order in their documentation.

The ISO section 7.1.3 you quoted is very reasonable and succinct, and contradicts your claim that explicit multiplication sign removes ambiguity. There would be no need for this section if a left-to-right rule existed.

i didn’t fully understand the article, but it was really interesting reading summaries & side discussions in the comments here!

i enjoy content like this that demonstrates how math is at its heart a useful tool for conceptualizing things vs some kind of immutable force.

Damn ragebait posts, it's always the same recycled operation. They could at least spice it up, like the discussion about absolute value. What's |a|b|c|?

What I gather from this, is that Geogebra is superior for not allowing ambiguous notation to be parsed 👌