Can maths help you find true love? Many may argue quite the opposite – that the mere mention of the beauty of a quadratic equation or the perils of a small sample size might be enough to curtail any romantic liaison. But when it comes to devising a strategy for approaching the dating game in today’s hectic world, mathematics can offer a much needed helping hand.
A maths teacher – let’s call him Eugene – is about to embark upon a series of dates. He is a busy man, so decides beforehand that over the course of the next 6 months he can feasibly meet 25 women. What should his plan of action be? Should Eugene stop his search at the first date he likes, or hold out in case the woman of his dreams comes along a little later?
Fortunately, a model is at hand – although it might not be quite the model Eugene is hoping for. It is possible to construct a mathematical model that allows us to devise an optimal strategy for this dating dilemma. First we need a few assumptions:
1. You can only date one person at a time
2. A dates ends with you “rejecting” or “selecting” the other person
3. If you “reject” someone, the person is gone forever – old flames cannot be rekindled.
4. You must decide on the number of people you plan to date beforehand
5. As you date people, you can only tell relative rank and not true rank. This means you can tell the second person was better than the first person, but you cannot judge whether the second person is your true love.
Who says romance is dead?
With these assumptions, Eugene must weigh-up two opposing factors: If he picks someone too early, he is making a decision without knowing what future dates might bring. Alternatively, if he waits too long, he leaves himself with only a few dates to pick from.
A lovely piece of mathematics involving calculus and the most amazing number of all (e) demonstrates that the most effective strategy in these circumstances is for Eugene to reject the first 37% of dates, and then choose the next one who is better than any person he has met before. This is true regardless of the number of dates Eugene plans to have.
This model can be applied to a wide variety of circumstances, including buying a house or attending university open days. It can also make a lovely classroom activity: get a random number generator to produce amounts between £1 and £1,000,000 (don’t tell your students these limits), generate one number at a time for 25 goes and challenge students to devise a strategy that allows them to leave with a decent amount of money more often than not.
Of course, there is one rather important flaw in Eugene’s plans. Having rejected the 37% of dates advocated by the model, Eugene then meets the love of his life – Wonda. The problem is that Wonda is on her first date, and hence she rejects Eugene by default. Mind you, if Eugene did ever meet a woman who also devised her dating strategy based on mathematical models, I think it would be a match made in heaven.