Here’s how maths can help you find the love of your life this Valentine’s Day

Today is Valentine’s Day. A day for star-crossed lovers to reaffirm their adoration, and for secret admirers to dare to gift the objects of their desires a token of their affection.

I will admit that I don’t buy in to Valentine’s Day. My jaded older self would tell you that it’s an overly commercialised made-up “celebration”, invented by greeting card companies to flog us mass-produced tat for extortionate prices.

But I was not always this cynical. One year I bought 30 bunches of daffodils and strung them up on lampposts and notice boards that marked my girlfriend’s route home. Every surface in the flat was covered with jars and cups full of the chirpy yellow flowers. Incidentally, this was also the year I discovered I had hay fever! It is surprisingly hard to give away 30 bunches of daffodils the day after Valentine’s.

Another Valentine’s Day I sent my girlfriend an equation in a card, with a note asking her to plot it on her graphical calculator. The equation plots out a curve known as a cardioid – a heart shaped curve. Let it not be said that love does not encroach into the world of mathematics.

Conversely, mathematics itself has something to say about the world of love – specifically, it might just give you the best chance of finding the right partner.

Before we get to that, though, let’s tackle a problem that seemingly has nothing to do with maths: what if you want to take your Valentine’s date out for a nice meal this evening, but can’t decide where to go? You’re both quite hungry, but you’d like to find somewhere nice, so you don’t want to dive into the first place you see.

You consider yourself a good judge, so you’ll be able to rank the quality of each restaurant relative to the others. You figure you’ll have time to check out up to 10 restaurants before your date gets fed up with traipsing around. Because you don’t want to look indecisive, you decide that you won’t go back to a restaurant once you have rejected it.

The best strategy for this sort of problem is to look at and reject some restaurants out of hand in order to get a feel for what’s out there. Once you’ve judged a number of restaurants, you can choose the first one you see that’s better than all the others you’ve looked at so far.

This is called an optimal stopping strategy. Once you’re happy with the strategy, the question becomes: how many restaurants should you look at and reject, just to get a sense of what’s on offer? If you don’t look at enough, then you won’t get a good feel for what’s available – but if you rule out too many before taking the plunge, then your remaining choice is limited.

The maths behind the problem is complicated, but it turns out you should judge and reject roughly the first 37 per cent of the restaurants (rounded down to 3 if there are only 10) before accepting the next one that is better than all the previous ones.

But what if the best restaurant was in the first 37 per cent? In this case you miss out. The 37 per cent-rule doesn’t work every time: it’s a probabilistic rule. In fact, this algorithm is only guaranteed to work 37 per cent of the time. That’s the best you can do given the circumstances, but it’s better than the 10 per cent of times you would have chosen the best restaurant if you had just picked the first of 10 at random, and way better than the 1 per cent success rate if you had to choose at random between 100 restaurants. The relative success rate improves the more options you have to choose from.

The optimal stopping rule doesn’t just work for choosing restaurants. You can use it to get the best seat on the train or to choose the shortest queue at the supermarket. And if you’re clinical enough, you can even use this algorithm to tell you how many people to date before you decide to settle down.

You first need to decide how many partners you think you might get through by the time you’d like to get out of the dating game. Perhaps you might have one partner a year between your 18^th and your 35^th birthdays, making a total of 17 potential partners to choose from. Optimal stopping suggests that you play the field for about six or seven years (roughly 37 per cent of 17 years) trying to gauge who’s out there for you. After that, you should stick with the first person who comes along who’s better than all of the others you’ve dated so far.

Understandably, not many people are comfortable with letting a predefined set of rules dictate their love life. What if you find someone who you’re truly happy with in the first 37 per cent? Is it wise to cold-heartedly reject them because you’re on an algorithmic love mission? What if you follow all the rules, and the person you decide is best for you doesn’t think that you’re the best for them? What if your priorities change halfway through?

Fortunately, in matters of the heart – as with other more obviously mathematical optimisation problems – we don’t always need to look for the very best solution. We don’t always need the single person who is the perfect fit. We don’t always need “The One”.

There are likely to be multiple people out there who will be a good match for us, and with whom we can be happy. As much as it pains me to say, maths doesn’t always hold the answers to all of life’s problems.