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On a Tuesday afternoon, I decided to have my usual 'self-study' period in my favourite Mos Burger, the one at Raffles Place. I was minding my own business eating my Mos Spicy Cheeseburger till I just realize there was a couple sitting to my right. They were certainly not a happy couple. The girl was holding the guy's hand but both of them were pouring tears. I could immediately sense that they were on the verge of a break-up and a major one at that. The guy was murmuring to himself, possibly confessing his unconditional love for the girl and the girl pulled endless sheets of tissue paper to wipe her tears. From the little conversation I could make out *okay I admit, I was eavesdropping a bit*, I suspected the girl was in the wrong.


Anyways, from that short episode of a drama-type serial, I started contemplating what makes a good relationship, well, in a mathematical sense. Allow me to elaborate.

We are all familiar with polynomials and their roots. For those who are unfamiliar, it's quite easy to understand if you know some simple mathematics. A polynomial is basically an expression of a single unknown, usually x, raised to different powers and combined with constants. For example,  is a polynomial of degree 3 because the highest power of the x term is 3. A root of a polynomial is a value of x such that when we substitute this value into the polynomial, we get , or in graphical terms, the graph interests the x-axis. The maximum number of roots, there can be more than one, is equal to the degree of the polynomial and finding a root is usually called ‘solving’ for x.

Here comes my theory. Every boy-girl relationship (I usually don’t like that term, but heck) can be characterized by a polynomial equation and the number of roots for that equation tells how good or compatible the relationship is. Roots here can be analogous to ‘solving’ the relationship and couples want to have more solutions than problems right.

So it begs the question. What is the polynomial of my relationship? Well, it’s quite simple really. First, both individuals must find their own polynomial, an equation relating an independent variable x which represents various values or view on things to a dependent one y which measures how strong the view on that certain x.

When the boy and the girl has their own polynomial, they can now add them together to get the polynomial equation for their relationship and then see how many root’s are there, points where the graph meets the x-axis.

Let’s see an example. John has the polynomial  and Ginger has . So their relationship polynomial is . So how well does John and Ginger pair up? Graphing it out, we see that there are no roots. The relationship is NOT going to work! They should break up immediately. I better tell the guy to save his money on the presents. :-)


Is mathematics so cruel?! No. On the contrary, here is where mathematics saves the day. Fortunately, there is another way to make the relationship work out. The individual polynomials can be combined through means other than addition – namely subtraction, division and multiplication.

Suppose Ginger decides to subtract her equation from John’s to give the polynomial . This could mean that now Ginger is spending more time with John and by this we find that there are 2 roots. Of course the relationship will improve. See how much is achieve by spending time with your partner. But the two are still not satisfied and now John decides to divide his equation into Gingers by sacrificing some of his values to meet Ginger’s expectations. This gives them the polynomial    . Unfortunately, this move yields nothing as there are still 2 roots. Hmmm, I suspect that sacrificing your moral values to suit your partner is futile.

Finally, John and Ginger work together to edifying each other’s personality and values or equivalently multiplying their polynomials to give . Woah! The relationship skyrockets as shown by 4 roots. John and Ginger live happily ever after. I guess it really pays to do what is in the best interest of your partner, regardless whether it benefits you or not.

I for one DON'T have a girlfriend and plan not to anytime soon. Haha, perhaps it's because no girl would want a guy who use mathematics to explain relationships. Damn.