Why is it BODMAS?

[Dilbertian]

Is BODMAS something that was agreed upon or imposed in order to make mathematics uniform, or does it have a mathematical reason why it has to be?

Eh? I thought it was just the way you had to work it out? So do brackets first etc etc.

Yes, it's order of precedence of mathematical calculations.

I thought it was BOMDAS. I was good at Maths though obviously not.

It’s a good question though. As to *why it’s in that order!

Isn't it a great question. Perhaps everything we know maths to be is just because of this convention and perhaps we're all wrong, all of the time!

It's either - you do brackets, then indices, then multiplication and division in order through the calculation, then the same with addition and subtraction.

Division is the same as multiplication by a fraction, so they're effectively the same thing.

Subtraction is adding a negative number, so addition and subtraction are the same

hmm, I think you are confusing the unchanging reality of maths, with the language we use for describing it. The latter is just a convention for communication. The former is reality and unchanging

In answer to why, there just needed to be a rule to make it consistent. If it had been BOASMD, we'd just use brackets in different places to get the calculation done in the correct order for whatever we're doing

So under bodmas we'd write 5 x 7 + 2 / (3-1) = 36

Under boasmd we'd write (5 x 7) + (2 / 3 - 1) = 36

Why is 2+3x4=14 right, but 2+3x4=20 is wrong?

Because multiplication takes precedence over addition, I think.

To make the answer 20, you'd need to put the 2+3 in brackets.

As @123ZYX said, it was agreed so that equations could be understood by different people. There's no real reason it had to be that order.

It's like spelling, "would" and "wood" didn't have to be spelt differently, but it makes things easier if we agree they are.

It’s because multiplication is repeated addition
5 x 2 = 2+2+2+2+2
orders(=powers, indices, exponents) are repeated multiplication
5^2=5x5
so you’re kind of doing the higher level ones first, and then brackets can override it as you need

Convention I believe. I think there might be some nice properties for vectors or matrices with that order of precedence but I wouldn’t be surprised to hear those properties could be found in any order. But my group theory is rusty!

There is no mathematical reason it has to be.

It was just agreed upon, a bit like spelling.

That makes sense.

So 2+3x4 can be simplified to 2+3+3+3+3, which wouldn't work if you simply did the operations in order from left to right.

Multiplication is also scaling.

addition/ subtraction are inverses as are multiplication/division
And yes we also need the convention for consistency
just for completeness

Yes

Who made the rules? Like it's not in the bible is it?

That argument is circular though. 2+3*4 could have been written as 2+3+2+3+2+3+2+3 with a system that has addition operation that has precedence over multiplication. You need BODMAS to get that expansion. BODMAS is clearer which is why we use it but we can make the notation mean anything so we agree on the rules for clarity.

I find it difficult to believe that the order of operations is merely a convention because maths was discovered by many cultures, in many languages. Some read left to right, some read right to left, some read top to bottom, some even pallindromically, switching direction every line. Yet AFAIK for all of them 2+3x4=14.

The convention that seems to have been imposed worldwide is that maths in Western digits reads overall from left to right. I wonder, in right-to-left-reading languages with different numerals, does maths also read right to left?

It’s a nice convention. But you’re not asking about maths you’re asking about how we write it down. Not quite the same thing!

Hmmm that didn’t come across how I wanted to.

When we use BODMAS what we are actually doing is saying “I’m not going to put all the bloody brackets in all the time.” So it’s just a convention or where the “invisible” brackets are.

When I was at school there was no BIDMAS or BODMAS and we just set things out properly used brackets to make it clear what we were doing.

In fact, that's what we did during my maths degree as well.

I still think it would be much clearer to just use brackets, because 2+(3x4) or (2+3)x4 is clear to everyone what it means, whereas I have to stop and think about what 2+3x4 means.