*Has The Mathematics of Love by Hannah Fry been sitting on your reading list? Pick up the key ideas in the book with this quick summary.*

*her*love into, revealing what mathematics can tell us about the secrets of lasting relationships. From your odds of finding “The One” to the way that game theory can reveal the best pick-up strategies, this book summary will take you on a journey of math and love, and the way they influence each another.

In this summary of The Mathematics of Love by Hannah Fry,You’ll also discover:

- how alien civilizations and “The One” are related;
- what bidding can enlighten us on about dating; and
- why 37 percent is considered a magic number.

# The Mathematics of Love Key Idea #1: Calculating Our Chances of Finding A Partner

The search for romantic love can leave us feeling somewhat hopeless at times – like the odds are against us. Mathematician Peter Backus was one of these discouraged bachelors. In 2010, Backus went as far as to prove that there were more intelligent*alien civilizations*in existence than there were potential girlfriends for him! His conclusion was based on calculations guided by the following questions: How many women live near me? For Backus who was living in London, that answer was four million. How many are likely to be of the right age range? This total came to 20 percent or 800,000 women. How many are likely to be single? That amount of women was 50 percent or 400,000. How many are likely to have a university degree? This would be 26 percent of the women or 104,000. How many are likely to be attractive? He calculated that to be five percent or 5,200 women. How many are likely to find me attractive? Again, this was calculated to be five percent or 260 women. Finally, how many am I likely to get along well with? And this was ten percent or 26 women. This left Backus with only 26 women available for him to date. Comparatively, scientists currently estimate there to be about 10,000 intelligent alien civilizations in our galaxy. But if Backus had been slightly less picky and relaxed his criteria, he would’ve had a substantially larger pool of potential partners. For example, he assumed he would only get along with one in ten women that he met. If he increased that percentage to 20 percent, raised the amount that he found attractive to 20 percent, and bumped up the rate of women who would find

*him*appealing to 20 percent as well, he’d be left with a more optimistic total of 832 potential partners. In love, it pays to be somewhat flexible with criteria. As luck, or perhaps math, would have it, Backus did eventually tie the knot in 2014.

# The Mathematics of Love Key Idea #2: Mathematical Concepts Linked to Beauty

We all know that beauty is supposed to be in the eye of the beholder, but there are a few people whose faces are so attractive, they seem to be almost unquestionably beautiful or handsome. Therefore, there must be some essential criteria for evaluating beauty that we all agree on. Some people believe beauty is encoded in the mathematical concept known as the*golden ratio*, which has been frequently applied to human attractiveness. The golden ratio is a number roughly equal to 1.61803399 and usually denoted by the Greek letter

*phi*or

*Φ*. However, this theory doesn’t hold up exceptionally well. You may have heard, for instance, that the “perfect” face should include a mouth 1.618 times larger than the base of the nose, eyebrows 1.618 times wider than the eyes, and so on. But the predicament in applying the golden ratio is, if you’re looking for a pattern, you’re very likely to find one, especially if prepared to be reasonably lax with your definitions. For example, how do you define where your ear starts or precisely the point where your nose ends? Golden ratio aside, some mathematical ideas do appear to be correlated with beauty. One of these concepts is our inclination for average face shape. Researchers have long understood that overlaying images of many faces from a given ethnic group leads to an average face that is generally considered attractive. The theory behind this preference is that when searching for a potential partner, we tend to be disinclined to unusual face shapes. That is because they may indicate a genetic mutation that we don’t want to pass on to our offspring. Facial symmetry is another significant factor for attractiveness, and those with more symmetrical faces consistently score highly on attractiveness surveys.

# The Mathematics of Love Key Idea #3: Why it Isn’t Always Best to Go for the Most Attractive Person

You’re single and at a party: should you wait for someone to approach you first, or go right up to the most attractive attendee, chat them up and risk rejection? Well, according to the Nash Equilibrium, it’s not the brightest idea to make a beeline for the person you are most attracted to. Maybe you’ve seen the film*A Beautiful Mind*, which tells the story of famous mathematician John Nash. In one famous scene, Nash and three of his male friends spot a group of five women in a bar: four brunettes and one stunning blonde. All of the men are immediately drawn to the blonde, but instead of tripping over each other to get to her, Nash suggests a tactic based on mathematics that would accommodate all of their the best interests. His theory of equilibrium states, if they all went for the blonde, they’d block each another, resulting in none of them going to bed with her. However, if none of them approached her, they wouldn’t get in one another’s way

*and*wouldn’t insult the other women by making them feel like the second choice. So, the conclusion was to approach the four brunettes. Sometimes it is beneficial to approach the person you’ve singled out. At a party, if you do all the asking, risking continual rejection, you end up better off than those who wait for everyone to come to them. If you begin at the top of your list of people you’d like to hook up with and work your way down, you’ll end up with the best viable option which accepts your advances. If alternatively, you wait for people to talk to you, you’ll get the least preferable person who approaches you.

# The Mathematics of Love Key Idea #4: Why Dating Website Algorithms Cannot Accurately Predict Compatibility

Attending too many parties in a row can drain your energy for meeting potential partners, so what about online dating? Dating websites apply specific algorithms to calculate how compatible people are with each other. OkCupid is a free website founded by a group of mathematicians, based on a particularly sophisticated algorithm that creates a score to determine how well people match. The key ingredients are what your responses are to a questionnaire, the answers you’d like a partner to give, and how important each question is to you. The value system for your questions are as follows: Not at all important = one, A little important = ten, Somewhat important = 50, Very important = 100, and Mandatory = 250. Let’s demonstrate the process with two fictional characters, Harry and Hermione and two questions: “Do you like quidditch?” and “Are you good at defeating dark wizards?” First, the algorithm determines how good of a match Hermione is for Harry. Let’s say Harry answered the first question with “Yes,” rating it as “A little important.” and Hermione responded to that question with “Yes” as well. That would mean she receives ten out of ten possible points. But then, if she responded to the second question with “No,” while Harry wanted his match to answer “yes” with a rating of “Very important” for that question, she’d get zero out of 100 possible points for that question. The result of Hermione’s total match percentage for Harry would be (10+0) / (10+100) = 10/110 = 9.1 percent. Finally, the algorithm would calculate Harry’s match percentage for Hermione and average it. But even the most elegant algorithms frequently fail to predict our compatibility with others accurately. If the internet were the ultimate matchmaker, there wouldn’t be so many people still suffering through terrible dates. The flaw is, using*individual*data to predict how well people will get along often doesn’t work. Two personalities may both love Harry Potter movies, but that doesn’t honestly tell us anything about if they would enjoy watching them

*together.*

# The Mathematics of Love Key Idea #5: What Game Theory Reveals

So you meet someone, and the sparks are flying; are there some mathematical rules that could help you get what you want? Well, try game theory. Game theory applies best to men with just one thing on the mind. If you’re a male, dead set on persuading women to sleep with you, mathematicians Peter Sozou and Robert Seymour can help. Sozou and Seymour’s approach requires the assumption that you have a range of offerings at your disposal, like flowers or a candlelit dinner. Your tactic, then, should be to go for the gifts most likely to get you what you want without attracting women who only want the rewards. In game theory, the woman is viewed as an opponent, whose task is to win the best man using sex as her means of bargaining. Here’s how the strategy works: to impress the woman in question, choose gifts with a high value, but still must be shared to have any meaning. So a candlelit dinner, fancy firework display or pulling up to her house in a fancy car would all be excellent options, but buying her jewelry would not. Game theory also posits that women should refrain from getting complacent when looking for a partner. Dating can be seen as the mathematical equivalent to an auction, where bidders submit bids. Now, it may appear that the strong bidder, or in this case, the most attractive woman, has the highest chance of acquiring the man. But it’s often the bidder in the weaker position who comes out on top. Why is that? Because when a weak bidder finds a man that she likes, she’ll do everything to attract his attention. A confident bidder, however, is less likely to make too much of an effort and is, therefore, less likely to get the man as well.# The Mathematics of Love Key Idea #6: Our Number of Sexual Partners, Math, and Sexually Transmitted Diseases

Once you’ve found a person you connect well with romantically, the matter will probably progress to the bedroom. Fortunately, mathematics can offer us some helpful tips there, too! The amount of sexual partners we have is not random, interestingly enough. In 1999, Swedish sociologist Fredrik Liljeros and a team of mathematicians discovered a formula that can determine the number of sexual partners we’re likely to have over our lifetime. Many would think that this falls under the normal bell curve distribution, similar to height or IQ, but the formula instead follows the*power-law distribution*. The way that we form networks on Twitter is an excellent way to understand the power-law distribution. Most people on Twitter have roughly the same number of followers, but some have a vast amount. For example, Katy Perry with her 57 million followers, is the biggest hub on the Twitter network. Like with Twitter followers, most people have about the same number of sexual partners, but there are some who’s is significantly higher. What can we do with this information? Well, mathematical knowledge of sexual networks can reveal how sexually transmitted diseases are spread. Those who have a high number of sexual partners create focus points in the sexual network and are the critical players in disease transmission. But how can we find these people? Let’s return to the topic of Katy Perry’s Twitter presence for a moment. If we were to select someone at random from the 500 million people on Twitter, we’d have a one in 500 million chance of finding Katy. But, if instead, we chose someone at random and asked them to show us the most famous person they follow, it’d bring us to Katy 57 million times. Therefore, we’d have about a ten percent chance of finding her. This important rule has been applied in anticipating the spread of epidemics.

# The Mathematics of Love Key Idea #7: How Many Potential Partners You Should Reject

Maybe you’ve been dating for a while, and it’s time to settle down now. The question is, how can you figure out the best person to settle down with if you can’t rule out possible partners you have yet to meet? That is where mathematics can help us again. In this situation, math can inform you how on many potential mates you should reject until you find the one that you want to commit to. It’s called the*optimal stopping theory*and it goes as follows: if you’re destined to date ten people over your lifetime, the formula dictates you have the highest chance of finding “The One” after you reject your first four partners. In doing that, the probability of your fifth partner being The One reaches a somewhat reasonable 39.87 percent chance. If more partners are in your cards – let’s say 20 – then you should call it quits after your first eight partners. At this point, the likelihood of Mr. or Ms. Right appearing in your life is 38.42 percent. Have you detected a flaw in this calculation method? Unless you’re a member of the English royal family during the 1500s, your potential suitors won’t be waiting outside your room, ready to be courted. There is just no way to ascertain precisely how many people you’ll date over your lifetime. But there’s hope for this model, and it lies in the number 37. Luckily, it’s enough only to know how

*long*you wish to date in your life. If you begin dating when you’re 15 years old, with the thought process of settling at 40, then you should reject

*every one*in the first 37 percent of your dating window, or in other words, until just after you turn 24. That provides you with a little over a one in three chance of finding your perfect match!

# The Mathematics of Love Key Idea #8: Optimizing Wedding Planning with Math

Let’s say you’ve found the love of your life and now it’s time to plan a wedding. But before you dive headfirst into all the unavoidable stresses, let’s see how mathematics can help. Close to the top of everyone’s list of stressors is the guest list: assembling a workable list of invitees can be a nightmare. Budgetary constraints and venue size may force you into uncomfortable situations, and of course, not everyone you invite will turn up the day of. Once again, mathematics can come to your rescue and assist you in more precisely anticipating the number of people who will be attending your wedding. First, list all the potential invitees grouped as couples or families. You can make that list into a spreadsheet, with the name of the group in the first column, and the number of people included in the group in the second column. Next, determine how likely it is that each group will show up if invited. For example, your best friend from home is 95 percent likely to attend, so they and their group would collectively get a score of 0.95. And you enter this score into the third column of the spreadsheet. Then, you multiply the number of people in each group by their score in the third column. That will give you a number for the fourth column which will contain the expected number of people who’ll accept the invitation. As you go down the list, maintain a running total of the expected number of guests in a fifth column. Using this system, you will, on average, invite the correct amount of people to your wedding, alleviating one of the biggest headaches of the planning process.# The Mathematics of Love Key Idea #9: Predicting How Likely a Marriage is to Last

Finding the person you want to settle down with is one of life’s greatest joys, but unfortunately, a lot of marriages don’t last. Wouldn’t it be helpful to know the best way to behave in a long-term relationship to maintain your wedded bliss? As you may have already guessed, there’s a formula for that! To be specific, there is a formula for predicting how positively or negatively a married couple will behave when it’s their turn to speak or act in a conversation. When looking at arguments, in particular, the way that couples argue can vary considerably and can be a useful predictor of long-term happiness. Psychologist John Gottman discovered a technique to score how positively or negatively a couple can behave toward each other. Gottman’s scoring system was surprisingly accurate, predicting divorces with up to 90 percent accuracy by merely observing a couple talking to each other. However, it wasn’t until Gottman teamed up with mathematician James Murray that he figured out how spirals of negativity in conversations are created. Murray created two similar formulas for both of the partners. These formulas allow us to calculate how positive or negative the next thing each person says will be. A wife’s response, for example, depends on her overall mood, her mood when with her husband, and the influence her husband has on her. If her husband acts somewhat negatively, like interrupting her when she’s talking, he’ll negatively impact his wife. Through this formula, we can determine at which point the husband is amply negative to change his wife’s mood, resulting in a possible breakup. Interestingly, Murray’s equations have also been shown to successfully explain what occurs between two countries during an arms race.## The Mathematics of Love Key Idea #10: In Review

The key message in this book:**From online dating to understanding the spread of sexually transmitted diseases, mathematics gives us insights that get rid of some of the mysteries of love and provides us with the best chance of finding “The One.”**Actionable advice:

**Make them love you or loathe you.**When people pick their online dating profile pictures, they often hide aspects that may make them come off unappealing, by using cropping techniques for example. But that’s the opposite of what you should do. People who are exceptionally good looking are always going to be flooded with messages, but it would be beneficial for the rest of us to divide opinion rather than aim to look as attractive as possible. Statistical analysis has determined that people who elicit polarizing opinions regarding their looks end up being considerably more popular on internet dating sites than those that everyone finds “quite cute.” So when choosing your profile picture, play up to whatever features make you different – including the facets that some people might find off-putting!

**Suggested further reading:**

*Dataclysm***by Christian Rudder**

*Dataclysm*explains what data collected on the internet can inform us about the people who use it, as opposed to the information gathered from the more sterile environment of a scientific laboratory. What you’ll learn from this is not all pleasant: when we think no one’s watching, we tend to behave in nasty, brutish ways.