The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation

by Hannah Fry

Mathematics is the language of nature. It is the foundation stone upon which every major scientific and technological achievement of the modern era has been built. It is alive, and it is thriving.

Paul Davies puts it: No one who is closed off from mathematics can ever grasp the full significance of the natural order that is woven so deeply into the fabric of physical reality.

This is known in economics as the “decoy effect.” What it demonstrates is that the presence of an irrelevant alternative can change how you view your choices.

Despite the name, game theory isn’t just about studying activities undertaken for amusement. It can apply in any situation where two or more adversaries compete against one another for some sort of payoff.

This setup is known as the “stable marriage problem,” and the process through which the friends picked their partners is called the Gale-Shapley algorithm.

In short, the group who do the asking and risk continual rejection actually end up far better off than the group who sit back and accept a suitor’s advances.

If you put yourself out there, start at the top of the list, and work your way down, you’ll always end up with the best possible person who’ll have you. If you sit around and wait for people to talk to you, you’ll end up with the least bad person who approaches you. Regardless of the type of relationship you’re after, it pays to take the initiative.

If you can handle the occasional cringe-inducing rejection, ultimately, taking the initiative will see you rewarded. It is always better to do the approaching than to sit back and wait for people to come to you. So aim high, and aim frequently: The math says so.

(Hermione’s match percentage × Harry’s match percentage)^(1/2) Or (99.6 × 9.1)^1/2 = 30.1% match.

Messages = 0.4 a1 - 0.5 a2 - 0.1 a4 + 0.9 a5 +k

Put this list in a spreadsheet, with the name of the group in the first column, and the number of people the group represents in the next. The next step is to decide how likely each group of people is to actually show up if you invite them. Think about how far away people live. What else is going on in their lives? Do they secretly hate you? You get the idea. Think in terms of a percentage but write it down as a decimal. For example, your close friend from home and her boyfriend might be 95 percent likely to attend, so they would collectively get a score of 0.95. This makes up the third column of your spreadsheet. Multiplying the second column—the number of people in each group—by their score in the third column gives you a fourth column containing the “expected” number of people who will RSVP with a yes. As you go down the list, from the VIPs to the also-rans, keep a running total of the expected number of guests in the fifth column. The simplest method is then to set the cutoff once the running total of expected guests exceeds the capacity of the venue. By doing this you will, on average, invite the right number of people to your wedding. The table on the following page gives you an example of how the bottom end of this spreadsheet might look. With a venue that can host one hundred guests, you should invite everyone up to Gordon and family. You’ll send out invitations to more than one hundred guests, but on average you can expect only one hundred to arrive. Unfortunately...

Wt+1 = w + rwWt + IHM (Ht) Ht+1 = h + rHHt + IHM (Wt)

The most successful relationships are the ones with a really low negativity threshold.4 In those relationships, couples allow each other to complain, and work together to constantly repair the tiny issues between them. In such a case, couples don’t bottle up their feelings, and little things don’t end up being blown completely out of proportion.