The Mathematics of Love: Three Patterns in Romance

Level: B2

Printable: Student handout (PDF | Word) | Teacher’s key (PDF | Word)

Before You Read

Think about these questions or discuss them with a partner.

What do people usually look for in a partner? Make a short list of three things.
How do people in your country usually meet partners: through friends, family, school or work, or apps?
How might ideas about when to choose a long-term partner differ by country, age, or personality?

Reading

You open a dating app and set your filters: age, city, education, perhaps height. Each filter you add makes the list of possible partners shorter. An economist once took this idea to its comic limit. Using a formula that astronomers use to estimate how many alien civilizations might exist, he narrowed down a pool of about thirty million women to roughly 26 who matched his wishes. It was a stunt, of course, since love does not work like a spreadsheet. Still, it raises a fair question: can mathematics tell us anything useful about romance? Mathematicians say yes, and three of their findings stand out.

The first finding concerns online dating. One dating site compared how men rated women’s looks, on a scale of one to five, with the number of messages the women received. You might expect the highest average score to win, but it did not. Among women with similar averages, those with the most divided ratings, loved by some men and disliked by others, received the most messages. A profile that polarizes opinion beat one that everyone found pleasant but unremarkable. The site’s explanation was that people hesitate to approach someone they expect everyone else to want, but feel braver when they sense little competition.

The result has limits. It comes from one site, one city, and a narrow age group, and it shows a link, not a cause. The explanation is the company’s own guess. Even so, the practical lesson is interesting. Many people downplay what they fear others will dislike, with a cropped photo or a hat, for example. The data hints that this may backfire: the people who like what makes you different will contact you, and those who do not were never going to.

The second finding concerns timing. When should someone stop looking and commit? Mathematicians studied a version of this puzzle and found a clear rule: spend the first 37 percent of your search only looking, rejecting everyone as a serious candidate. Then choose the first person who is better than everyone you have met so far. Under the puzzle’s rules, no strategy gives a better chance of ending up with the best person overall, yet even this one works only about 37 percent of the time. If you plan to date for twenty years, the rule says to wait about seven or eight before choosing.

The rule has obvious risks. Your ideal partner might appear during the looking phase and be rejected. Or you might meet a run of disappointing people and then settle for someone only slightly better. Real life also breaks the puzzle’s assumptions: you do not know how many people you will meet, you cannot rank people on a single scale, and you can sometimes return to someone you passed over. In experiments, people tend to stop searching too early, so the rule’s real value may be as a reminder to explore first.

The third finding concerns staying together. The psychologist John Gottman recorded hundreds of couples discussing disagreements, measuring their words, facial expressions, and heart rates. How positive or negative each partner was turned out to be an important predictor of trouble. Working with the mathematician James Murray, he then built equations to predict each partner’s next response. They depend on each person’s mood alone, their mood with their partner, and how strongly the two influence each other. One term is the “negativity threshold”: how much irritation a person will tolerate before reacting. You might expect that letting small things go is best, but the model suggested the opposite. Couples who last tend to have a low threshold. They notice problems, say so, and repair them. Couples who stay silent can slide into a spiral, where each unkind remark provokes another.

Treat all of this with care. Gottman’s team has claimed that its methods can predict divorce with more than 90 percent accuracy, but critics point out that predictions that work well on the couples used to build a model often work much worse on new ones. The same caution applies to the popular idea that half of all marriages end in divorce. Recent US estimates for first marriages are closer to four in ten, though the figure depends on who is counted and when. Next time a small disagreement appears, notice whether you speak up or stay silent. That choice is exactly what the negativity threshold describes.

Vocabulary

Each word has a frequency score, a rank, and a tag. The score shows how common the word is in modern English: higher means more common, and each full point means roughly ten times more common. The rank is the word’s position on a list of about 321,000 English word forms, from most to least common. The tag shows where you are most likely to meet the word: Current, Formal, Literary, or Dated. The paragraph number shows where the word first appears in the reading. The labels are information, not instructions. Deciding which words are worth your time is up to you. How to read the scores, ranks, and tags.

An economist used a formula to estimate how many women matched his wishes.
Can you estimate how long the trip will take?

The economist narrowed down thirty million women to roughly 26.
We narrowed down the list of hotels to two.

The writer calls the economist’s calculation a stunt.
The shop gave away free pizza as a publicity stunt.

A profile that polarizes opinion can receive more messages.
The new law polarizes the country.

A pleasant but unremarkable profile may receive fewer messages.
The hotel was clean but unremarkable.

People may hesitate to approach someone they think everyone else wants.
Do not hesitate to ask if you need help.

Many people downplay what they fear others will dislike.
The manager tried to downplay the mistake.

The puzzle asks when someone should stop looking and commit.
She was not ready to commit to a long contract.

You might settle for someone who is only slightly better than the last person.
We wanted a sea view but settled for a room by the road.

Real life breaks the puzzle’s assumptions.
The plan failed because its assumptions about customers were wrong.

The negativity threshold is how much irritation a person will tolerate.
I cannot tolerate loud music at night.

The equations measure how strongly partners influence each other.
Friends can influence the music you choose.

Couples who last notice problems, say so, and repair them.
He used glue to repair the broken cup.

Silent couples can slide into a spiral of negativity.
Rising prices can send an economy into a downward spiral.

In a spiral, each unkind remark provokes another.
A rude joke often provokes an angry answer.

Word Partners

Collocations. Match the two halves to make common phrases. Then use three of the phrases in sentences of your own.

1. a rough	a. to a long relationship
2. a publicity	b. second best
3. hesitate	c. stunt
4. downplay	d. estimate
5. commit	e. the risks
6. settle for	f. spiral
7. a downward	g. a damaged friendship
8. repair	h. to ask for help

Answers

a rough estimate (d)
a publicity stunt (c)
hesitate to ask for help (h)
downplay the risks (e)
commit to a long relationship (a)
settle for second best (b)
a downward spiral (f)
repair a damaged friendship (g)

Word families. Complete each sentence with the correct form of the word in brackets.

She answered the question without any __________. (hesitate)
Good teachers show __________ toward students who have different views. (tolerate)
She is one of the most __________ writers of her generation. (influence)
Do not __________ that everyone agrees with you. (assumptions)
His __________ comments caused an angry reply from the crowd. (provokes)
They made a serious __________ to each other. (commit)

Answers

hesitation
tolerance
influential
assume
provocative
commitment

Activity Page

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Speed Challenge

Answer 12 questions against the clock. Every wrong answer adds 5 seconds, and the lowest score wins. Open the speed challenge in a new tab.

Quick Reading and Typing: The Mathematics of Love in Brief

A shorter version of the reading that uses the lesson vocabulary. Read it for a quick introduction to the topic, or use it for reading aloud, shadowing (reading along with a model), and typing practice.

Mathematics can seem far from romance, but mathematicians say that love is full of patterns. An economist once tried to estimate his own chances of finding a partner. He used a formula that astronomers use to count possible alien civilizations. With it, he narrowed down about thirty million women to roughly 26. It was a stunt, since love does not work like a spreadsheet. Still, it raises a fair question about what numbers can tell us.

The first pattern concerns online dating. One dating site compared how men rated women’s looks with the number of messages the women received. The highest average score did not win. Women with the most divided ratings received the most messages. A profile that polarizes opinion beat one that was pleasant but unremarkable. The site’s own guess is that people hesitate to approach someone everyone else wants. The result comes from one site, so it is only a hint. Even so, it suggests that people should not downplay what makes them different.

The second pattern concerns timing. When should a person stop looking and commit? A famous puzzle gives a rule. Spend the first 37 percent of your search only looking. Then choose the first person who is better than everyone before. Even the best strategy finds the very best person only about 37 percent of the time. The rule also has risks. Your ideal partner might appear too early, or you might settle for someone only slightly better. Real life breaks the puzzle’s assumptions, for example, you cannot rank people on a single scale. The rule is better seen as a reminder to explore first.

The third pattern concerns staying together. The psychologist John Gottman recorded couples as they discussed disagreements. With the mathematician James Murray, he built equations that show how partners influence each other. One idea is the negativity threshold, which is how much irritation a person will tolerate before reacting. The model suggested that lasting couples have a low threshold. They speak up and repair small problems. Couples who stay silent can slide into a spiral, where each unkind remark provokes another. Gottman’s team has claimed that its methods predict divorce with more than 90 percent accuracy. Critics warn that such predictions often work worse on new couples.

How to practice

Read the text silently once and check any words you are unsure of.
Read it aloud slowly, one sentence at a time. On the typing page, the Listen button reads each line with your device’s voice, so you can listen first and then repeat.
Shadow: read aloud again at a natural speed, trying to keep a steady rhythm without stopping.
Record yourself, listen back, and note one sentence to practice again.
Type it on the typing page below and check your speed and accuracy.

Open the typing practice in a new tab

Comprehension Questions

What did the economist do with his formula, and why does the writer call it a stunt?
What did the dating site compare, and what did it find?
What explanation did the site offer for its finding?
Why should we be careful with this result?
What does the 37 percent rule tell you to do, and how often does it find the very best person?
What risks does the 37 percent rule have?
What does the reading say about real life and the puzzle’s assumptions?
What is the negativity threshold, and what did the model suggest about a low threshold?
Why do critics doubt the divorce predictions, and do you find their point convincing? Give a reason.

IELTS-Style Questions

True, False, or Not Given: “The economist later found a partner.” Explain your answer using the reading.
Yes, No, or Not Given: “The writer believes that the dating site’s explanation has been proved.” Explain your answer using the reading.
Author’s purpose: Why does the writer begin with the economist’s formula? Is it (a) to introduce a playful example before the serious findings, (b) to prove that astronomers are good at dating, or (c) to explain how dating apps work?

AI Discussion Prompt

I just read an article about the mathematics of love. It covered an economist’s joke estimate of how many partners match his wishes, a dating site’s finding that divided ratings brought more messages, the 37 percent rule for deciding when to commit, and a psychologist and a mathematician who built equations for how couples argue. I am an English learner at about B2 level. Please ask me one question at a time, starting with how people in my country usually meet partners. Respond to my ideas first, then briefly correct any language errors, and ask follow-up questions that make me explain my reasons.

AI Vocabulary Prompt

I want to practice vocabulary from an article about the mathematics of love. Please quiz me on the following words one at a time, using a mix of question types: multiple choice, true/false, and sentence completion. Give me feedback after each answer before moving on, and bring back the words I miss later. Here are the words: estimate, narrowed down, stunt, polarizes, unremarkable, hesitate, downplay, commit, settle for, assumptions, tolerate, influence, repair, spiral, provokes.

Discussion Questions

Have you ever used a dating app or website, or do you know someone who has? What was the experience like?
Do you prefer to meet new people through friends, at work or school, or online? Why?
What would you put in an online profile to show what makes you different?
Do you tend to speak up when something small bothers you, or stay silent? What usually happens next?
Why might a profile that divides opinion get more attention than one that everyone likes?
Many people choose their best photo for a profile. Is that honest, or does it give a false picture?
Does the idea of exploring first and choosing later sound sensible to you? Why or why not?
At what age do people in your country usually start looking for a long-term partner, and has this changed?
In experiments, people tend to stop searching too early. What pressures might push them to do that?
Would you want a mathematician to calculate your chances in love? What would be the benefit and the risk?
In some cultures, families help people meet partners. How might the 37 percent rule apply, or not apply, there?
Can numbers ever capture something like love? What might they miss?
Predictions that work on old data can fail on new data. Where else have you seen this problem?
Is it fair for dating sites to analyze their users’ data and publish the results? Where should the limits be?

Language Focus: Approximating Numbers and Amounts

What it is: Words such as about, roughly, nearly, only about, more than, and closer to show that a number is not exact. They come directly before the number.

Why writers use it: Writers often do not know an exact figure, or an exact figure would not help the reader. An approximation word is honest about this and keeps the sentence easy to read.

Examples from the reading:

“…a pool of about thirty million women to roughly 26 who matched his wishes.”
“…even this one works only about 37 percent of the time.”
“…predict divorce with more than 90 percent accuracy…”
“Recent US estimates for first marriages are closer to four in ten…”

Part A. Sentence starters Finish each sentence with a number and any other words, so that it is true for you.

I sleep about …
It takes me roughly …
I have nearly …
My phone has more than …
The place where I live has about …

Model answers

I sleep about seven hours a night.
It takes me roughly thirty minutes to get to class or work.
I have nearly two hundred photos of my friends on my phone.
My phone has more than fifty apps.
The place where I live has about two million people.

Part B. Questions Answer each question in a full sentence. Try to answer using about, roughly, nearly, or more than. Then ask a partner.

How many hours do you usually spend on your phone each day?
How far is it from your home to the nearest station or bus stop?
How many messages do you send on a normal day?
How much does a cup of coffee cost where you live?
How many people are in your class?

Model answers

I spend about four hours a day on my phone.
It is roughly a ten-minute walk from my home to the nearest bus stop.
I send nearly fifty messages on a normal day.
A cup of coffee costs about four dollars where I live.
There are more than thirty people in my class.

Online Resources

Secretary problem (Wikipedia). The puzzle behind the 37 percent rule, with its assumptions and success rate (paragraphs 4 and 5).
The math of beauty (Gizmodo). A report on the dating site’s analysis of looks ratings and messages received (paragraphs 2 and 3).
Marriage Math (Psychology Today). A magazine article on how Gottman scored couples’ conversations and how partners influence each other (paragraph 6).
Maths model tells if couple can go on ad infinitum (Times Higher Education). A 2004 news report on the model built by Gottman and Murray, including doubts from other psychologists (paragraphs 6 and 7).
Drake equation (Wikipedia). The astronomers’ formula for alien civilizations that the economist borrowed for his joke calculation (paragraph 1).