The Mathematics of Love

1. Mathematics reveals hidden patterns in human behavior, even love.

What I am, however, is a mathematician. And in my day job of teasing out and understanding the patterns in human behaviour, I’ve come to realize that mathematics can offer a new way of looking at almost anything – even something as mysterious as love.

Patterns in life. Mathematics is fundamentally the study of patterns, and these patterns exist not just in physics or weather, but also in human behavior, including the seemingly chaotic realm of love and relationships. From dating choices to long-term dynamics, mathematical models can provide unique insights.
Beyond emotions. While love involves intangible emotions, the actions and decisions surrounding it often follow predictable structures. By applying mathematical tools, we can analyze these structures and gain a different perspective on why we behave the way we do in romantic contexts.
Illuminating maths. The author's goal is not just to illuminate love through maths, but also to show how beautiful and relevant mathematics is by applying it to a subject often considered far removed from equations. It demonstrates that maths is a living, thriving language of nature and human interaction.

2. Calculating your chances of finding love involves breaking down criteria.

In fact, in 2010 mathematician and long-standing singleton Peter Backus even calculated that there were more intelligent alien civilizations in the galaxy than potential girlfriends for him to date.

Fermi estimation. Inspired by the Drake equation for estimating alien civilizations, mathematician Peter Backus used a similar method (Fermi estimation) to calculate his chances of finding a girlfriend in London. This involves breaking down the problem into a series of educated guesses about population size and filtering criteria.
Being too picky. Backus's initial calculation yielded only 26 potential partners, highlighting how restrictive criteria dramatically reduce the pool. The more "deal-breakers" you have, the closer your potential partner count gets to zero.
Relaxing criteria. Slightly relaxing criteria, such as geographical location or educational background, can significantly increase the number of potential partners. The key takeaway is that while preferences are natural, an overly extensive checklist can be self-sabotaging.

3. Beauty is complex, but perception can be influenced by mathematical principles.

Although many of these ideas are based more in science than mathematics, it’s worth knowing what you’re up against in the fight for affection and why beauty does go more than skin deep.

Beyond golden ratio. While the golden ratio is often cited, it's not scientifically supported as the definitive measure of beauty. Real mathematical and scientific links to perceived attractiveness include:

• Average face shapes (suggesting genetic health)
• Facial symmetry (indicating good development)
• Hormonal markers (like jawlines in men, full lips in women, linked to fertility)
  Personal preference matters. Despite universal tendencies, personal preferences play a huge role, often linked to desired personality traits. Faces can subtly signal assertiveness or easy-going natures, and people are drawn to faces that reflect the qualities they seek in a mate.
  The decoy effect. Discrete choice theory shows that irrelevant alternatives can influence perception. In dating, bringing a slightly less attractive friend (a "decoy") can make you appear more appealing by comparison, demonstrating that attractiveness is judged relative to available options.

4. Taking initiative in dating significantly increases your chances of success.

Regardless of the type of relationship you’re after, it pays to take the initiative.

Stable marriage problem. This game theory concept models how individuals with preference lists can be matched. When one group (e.g., men) does the approaching, they consistently end up with the best possible partner who will have them.
Waiting yields less. Conversely, the group that waits to be approached ends up with the least bad person who makes an offer. This highlights the mathematical advantage of being proactive rather than passive in seeking a partner.
Real-world application. The Gale-Shapley algorithm, derived from this problem, is used in various real-world matching scenarios, like assigning doctors to hospitals. The group doing the proposing consistently fares better, reinforcing the mathematical benefit of taking the lead.

5. Online dating algorithms have limits, but profile strategy matters.

The problem here is that you don’t really know what you want. So an algorithm that can accurately predict your compatibility with another person simply does not exist yet.

Matchmaking algorithms. Websites like OkCupid use algorithms based on questionnaires to calculate compatibility scores, filtering potential partners based on stated preferences and importance levels.
Questionnaires fall short. While useful for initial filtering, questionnaire-based compatibility doesn't reliably predict long-term success. People often don't know what they truly want until they experience it, and chemistry involves non-conscious signals like body language and language patterns.
Dividing opinion helps. Counter-intuitively, having some people find you unattractive on dating sites can increase your popularity. Users who divide opinion (some rate you very high, some very low) receive more messages than those everyone finds moderately attractive. This suggests playing up unique features in your profile picture is beneficial.

6. Game theory offers strategies for dating, but beware of cynical assumptions.

As neat an application of game theory as they are mathematically, they have one flawed assumption at their core: that men are trying to trick women into having sex with them and women are desperate for commitment.

Exploiting stereotypes. Some game theory applications to dating, like strategies for men to attract women without attracting "gold-diggers" or explaining the "eligible bachelor paradox," rely on cynical and stereotypical assumptions about gender motivations.
The eligible bachelor paradox. This theory suggests that less attractive women are more likely to "bid" aggressively for desirable men early on, taking them off the market and leaving a shrinking pool of men for more attractive women later.
Tit-for-Tat strategy. A more universally applicable game theory concept is the Prisoner's Dilemma, which models repeated interactions like relationships. The "Tit-for-Tat" strategy (be nice first, then copy your partner's last move) promotes cooperation and forgiveness, offering sensible advice for navigating dating conundrums without resorting to manipulation.

7. Sexual connections form a network with predictable mathematical properties.

Many things can happen when two people have sex for the first time: the start of a new life, the start of a new infection, intense mutual embarrassment and even, occasionally, pleasure. However, one thing always happens whenever two people have sex: they create a link between themselves in an imaginary network.

Power-law distribution. Surveys on sexual partners reveal a power-law distribution, meaning most people have few partners, but a small number have a disproportionately large number. This pattern is found in other networks like the internet and social media.
Scale-free networks. This distribution is characteristic of "scale-free" networks, which have "hubs" – individuals with many connections. In the sexual network, these hubs are crucial for understanding the spread of sexually transmitted diseases.
Targeting hubs. A mathematical trick allows finding these hubs without mapping the whole network: pick a random person and ask them to point to someone they've slept with. This method is much more likely to lead to a hub than picking randomly, offering a strategy for targeted STD prevention efforts.

8. Optimal stopping theory suggests a strategy for when to settle down.

When dating is framed in this way, an area of mathematics called ‘optimal stopping theory’ can offer the best possible strategy in your hunt for The One.

The Secretary Problem. This theory addresses how to choose the best option from a sequence when you can't go back to previously rejected options. Applied to dating, it helps determine when to stop looking for a partner.
The 37% rule. The optimal strategy is to reject the first 37% of potential partners (either by number or time) to get a feel for the market. After this phase, choose the very next person who is better than anyone you've met so far.
Risks and variations. While mathematically optimal for finding the absolute best, this strategy has risks (rejecting The One early, or settling for someone just marginally better than the initial bad batch). Variations exist for being happy with someone in the top 5% or 15%, which involve rejecting a smaller percentage initially.

9. Mathematics can help optimize wedding planning logistics.

But before you lose your mind staring at calligraphy fonts and organza chair bows, I want to try and show you how maths can help to make things go a little bit more smoothly on the big day.

Guest list estimation. Probability can help estimate guest attendance. By assigning a probability of attendance to each invited group and summing the "expected" number of guests, you can determine how many invitations to send to hit your venue capacity on average.
Managing uncertainty. To avoid being over capacity, you can calculate the probability distribution of potential guest numbers. This allows you to adjust the number of invitations sent to ensure a low probability of exceeding your venue's limit.
Table planning optimization. Seating guests to maximize overall happiness (or minimize conflict) is an optimization problem. By assigning scores for how well pairs of guests would get along, mathematical algorithms can efficiently search through the trillions of possible seating arrangements to find the best one, far exceeding manual capabilities.

10. Long-term relationship success is linked to managing negativity thresholds.

The most successful relationships are the ones with a really low negativity threshold.

Mathematical modeling of conflict. Equations developed by Gottman and Murray model how couples interact, showing that a partner's reaction depends on their mood, their mood with their partner, and the influence of the partner's previous action. These models are mathematically equivalent to arms races.
Influence and thresholds. The "influence" term shows how a partner's actions (positive or negative) affect the other. A key finding is the "negativity threshold" – the point where a partner's annoying behavior triggers a highly negative response.
Low threshold is key. Counter-intuitively, successful couples have a low negativity threshold. This means they address small issues as they arise, preventing feelings from bottling up and escalating into major conflicts. It emphasizes the importance of constant repair and open communication about minor annoyances.

Last updated: May 4, 2025