# How to cheat at maths – and make a fortune in the process.

Some time ago I heard a program on the radio where they were discussing a maths question, and everyone was getting the answer wrong. When I tried it, I too was apparently incorrect. Fortunately, I have a son who is a maths teacher, so I was able to email Simon for clarification. I’ve re-produced our entire exchange here, which I hope will amuse you, or at least give you an insight into what passes for normal conversation within our family:

Anthony: I heard this thing on the radio last night – they asked what is 6 plus 1 times 0 plus 2 divided by 2? I made the answer 1 (as did everyone in the studio), but then they had some maths professor woman come on spouting something about BIDMAS or BODMAS and saying that the answer is 7. Which I think means that mathematicians make up arbitrary rules either to demonstrate their superiority and confuse us mere mortals, or because they can’t actually read!

By the way I tried this sum on my calculator and the answer was seven, unless I hit equals in between each part; then it gave the correct answer of one!

Simon: This woman is clearly not a professor of linguistics. I’d argue that when spoken, there is an implied sequential order. Written down, yes, the multiplications would take precedence, then the divisions and finally the additions and subtractions. It’s a little bit of a false declaration, though – whilst this is the correct prioritisation, it’s only in Key Stage 3 that you really encounter purely numerical problems where this is a concern. In higher levels it’s all algebraic, and the order is more readily apparent.

Anthony: Are you testing me to see if I’m alert when you say that multiplications take precedence over divisions?

Actually, I think that Thomas Alfred Bidmas has a lot to answer for, he clearly invented a set of rules just to follow his name!  Before he came along I’m sure that everyone was completely happy to follow the bird-watchers’ three in, two out principal of mathematics. (You may need to ask me about that!).

Simon: …no, I’m being an idiot. In my defence, at the time of writing I hadn’t sat down since 10am…

I am now officially asking you about bird-watchers.

Anthony: If a person goes into a hide to watch birds, he/she will invariably be unlucky because the birds know (having watched the person arrive) that someone is in the hide and will stay well away.  However, because birds have no mathematical ability, not even counting, then if three people go into the hide and two come out, the birds assume that the hide is now empty and will happily go up to it and unwittingly perform for the remaining bird-watcher.

The same principal applies to how Cuckoos flourish, because the adoptive parents are unable to count the number of eggs they laid.

So, if Thomas Alfred hadn’t invented his cockamamie set of rules to fit his surname, then we would all be as happy as birds!

Simon: Just so you’re aware, all of this is going in a year 7 lesson at some point.

Anthony: Glad to be of help.  I trust that your lesson will include a concise biography of T.A. Bidmas or at very least a brief history of the ‘gang of three’.

Simon: C’mon. You *know* I’m not going to be able to help but ask for these things now.

Anthony: Okay, so here goes…

Concise Biography of Thomas Alfred Bidmas (ne Bodmas).

Bodmas was born in Grimsby in 1867.  The son of a fishmonger, he was an average student and was fully expected to follow into the family business.  However, Thomas was possessed of a persuasive personality and an audacious streak which somehow allowed him to scrape a pass in his exams which led him to Fitzwilliam College Cambridge where he read Mathematics.  His lack of any real ability quickly became apparent and he was shunned by the ‘Wranglers’ (the name given to those placed in the First Class in Part II of the Mathematical Tripos)1 and despised by his professors.

His time at Cambridge was marked by two events: He changed his name by deed poll to Bidmas (some mistakenly believe that this was because he was ashamed of his humble background but in fact it was out of vanity – see A Brief History of the Gang of Three) and he devised a system for solving maths equations which allowed him to cheat in his exams and to swindle money from the more gullible of his fellow students.

Expelled from Fitzwilliam before graduation, he considered returning to Grimsby where his system would allow him to make a killing in the fish market but he realised that he could make a far greater fortune by fleecing the rich and the noble in London.

He moved to the Capital where he was soon living a lavish lifestyle and enjoying the company of vast numbers of women of easy virtue.

Eventually his cheating ways caught up with him when he tried to con a leading member of the judiciary, and he was sent to Newgate Gaol where he died of syphilis at the age of thirty seven.

Meanwhile, back at Fitzwilliam, the masters of the college realised that using the Bidmas method was an effective way of making themselves look very superior to the general population and not only adopted the system into their teaching, but also promulgated it to the rest of the Mathematical world.

Despite having no valid application other than to cause confusion in an otherwise uncomplicated discipline, Bidmas continues to be taught to this day.

A Brief History of the Gang of Three

Whilst at Cambridge, Bidmas was generally ostracised by his fellow countrymen for his lack of ability and his constant attempts to ‘play the system’ and cheat in exams.  It was this that brought him to the attention of an American undergraduate called Josiah Thaddeus Pemdas who was like minded and keen, as he said, ‘to pull a fast one on the limey stuffed shirts’.

Together they worked on Bidmas’s (at that time still known as Bodmas) plan for devising an order of operations to arrive at a different answer to an equation than the one that would be calculated by following the operations in the order they were written.

They surmised that if they argued their case strongly enough, they would be given first class degrees purely for their ingenuity and because the examining board would not be able to work out if their answers were right or wrong.

All went well until they came to name their system2.  Unknown to Pemdas, Bodmas had steered the order of operations so that the system could be named after him. He explained that it should be known as BODMAS as in; Brackets, power Of, Division, Multiplication, Addition and Subtraction.  Pemdas became very angry, and said that it made no sense because it would really be BPDMAS and in any case if Addition was to come before Subtraction then Multiplication should come before Division.  It would be better, he argued, if it was Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction or PEMDAS.

Bodmas was having none of that and quickly changed his name by deed poll to Bidmas. Now instead of power Of he could use Indices, which he argued was far superior to Exponents. He also complained that parentheses are grouping symbols, not operation symbols.

However, by this time, Pemdas was recruiting as many people as he could to his cause, and had devised the mnemonic: Please Excuse My Dear Aunt Sally.

Bidmas retorted with a mnemonic of his own: Bugger Off Dull Mindless American Swine.

Pemdas scornfully reminded him that Bidmas had just changed his name so his crass offering didn’t work, and insisted that he would continue with his own system back in the States whether Bidmas liked it or not.

Bidmas snapped, and quickly came up with: Britons Ignore Doubly Moronic American System.

At about this time, a young man from New Zealand named Joshua Pema, who shared rooms with Pemdas and who had been party to all the discussions, suggested a compromise. He said that because Multiplication and Division had equal precedence, as did Addition and Subtraction, it would be better to shorten the name to PEMA which would be easier to remember without a mnemonic.

Bidmas and Pemdas looked at Pema in disgust, called him a simpleton and said that only an idiot from a land of sheep farmers who can’t count past three without guessing would be capable of making such a ridiculous suggestion.

Pemdas took his version back to the USA where he made his fortune and founded his own university, where his system is still in use today.

Bidmas died in Newgate Gaol (see above).

Pema went back to sheep farming in New Zealand.  He tried to introduce his version of the system, but it was mostly lost on his circle of friends who couldn’t count past three without guessing.

Simon is now suggesting that I write an unabridged biography of Bidmas. I’m tempted by the idea, but it would be quite a long way down the list of projects that I have in mind. If I do decide to go ahead with it, I will announce its completion in my newsletter.

Finally, if you came to this post looking for a get-rich-quick scheme, then I’m sorry to tell you that I have completely wasted your time!