LOVE IN EQUATIONS: Math points to three major factors for stable relationships

Joey Marthyna Baldoza

Relationships are shaped by emotions, memories, disagreements, compromises, and countless decisions made between two people, making the idea of reducing love to numbers seem almost contradictory.

Yet researchers have found that some of the patterns behind romantic relationships can be described through mathematics. But rather than attempting to calculate how much one person loves another, researchers have developed mathematical models that examine how feelings between partners change over time and how relationships respond to conflict, stress, and other pressures.

The model does not predict who will fall in love, identify a perfect partner, or guarantee lasting relationships. Instead, it explores why some relationships endure life’s challenges while others weaken over time, drawing on mathematical models of populations and dynamical systems, alongside psychological research on relationships. 

At the center of this approach are three major forces that influence the stability of a relationship: mutual attraction, the gradual weakening of feelings that can naturally occur over time, and the emotional responses partners give to one another. Together, these factors help explain how a relationship can strengthen, weaken, or recover when it encounters stress.

From populations to partners

The mathematical study of romantic relationships has an unlikely history. Some of the ideas now being applied to couples were originally developed to understand something far removed from romance: animal populations.

Thomas Malthus developed early mathematical models for population growth in the 18th century, while the Lotka-Volterra equations were later used to describe the changing relationship between predator and prey populations. Another concept, known as the Allee effect, describes what happens when a population falls below a certain critical level. Once the population becomes too small, its chances of remaining stable and surviving can decrease significantly.

Researchers found that a similar idea could be useful when studying romantic relationships. Instead of looking at the number of animals needed for a population to survive, researchers can examine whether a relationship has reached a minimum level of emotional strength needed to remain stable.

The pull between two 

The first factor is mutual attraction, the force that draws two people toward one another and helps establish a relationship. This can involve physical chemistry, emotional interest, affection, or simply the desire to spend time together. 

A conversation that lasts until three in the morning, a message that brightens an ordinary day, or remembering small details about someone can all reflect this initial connection.

But attraction alone does not explain why some relationships last. 

Couples who have been together for years may spend less time on elaborate dates and more time sharing meals, doing chores, or simply being in the same room. As familiarity develops, the intensity of a new relationship can naturally change.

When the spark settles

The second factor is the gradual weakening of feelings that can naturally occur over time. Early relationships are often marked by novelty and heightened attention, but some of that intensity may fade as partners become familiar with each other.

This does not automatically mean that love has ended. Long messages may become a simple “I’m home,” while elaborate dates become shared meals after work. What matters is whether the relationship can adapt as feelings change.

A 10-year study of couples found different trajectories in relationship satisfaction, including couples who maintained relatively high and stable satisfaction. This suggests that while some relationships decline in satisfaction, others can preserve a strong sense of connection over time.

The everyday response 

The third factor is how each person responds emotionally to the other. Unlike attraction, emotional responsiveness appears repeatedly in ordinary interactions.

A partner coming home after a difficult day and saying, “You wouldn’t believe what happened today,” is making an attempt to connect. The other person might put down their phone and listen, or respond with a distracted “I’m busy.” Neither moment seems significant alone, but relationships are shaped by thousands of these small exchanges.

Psychologist John Gottman describes these attempts as “bids” for connection. They can be as simple as sharing a story, asking for an opinion, showing something funny, or seeking affection. How partners respond to these moments can influence how connected they feel over time.

What happens after

Conflict is unavoidable in long-term relationships. Disagreements over money, responsibilities, communication, or everyday habits can place pressure even on stable couples.

The mathematical model therefore focuses not only on whether conflict happens, but on how the relationship responds afterward. 

Relationships also exist within circumstances that neither partner can fully control. Work, school, financial pressure, illness, family responsibilities, and other stressful events can weaken the connection between two people.

This is where the model’s three forces become interconnected. Attraction may draw people together, feelings may change with time, and emotional responses can either strengthen or weaken their ability to withstand outside pressure.

Love beyond equations

Despite what equations can reveal, mathematical models cannot account for every part of a relationship. The source notes that many existing models are based largely on Western relationships, while love can be shaped by culture, religion, socioeconomic circumstances, and generations.

People can also change. Therapy, commitment, personal growth, and conscious effort can alter the course of a relationship in ways that a mathematical model cannot predict with certainty. These models identify patterns and tendencies—not unavoidable futures.

The equations may show the path, but they cannot decide where two people will go. Love may have patterns that mathematics can illuminate, but the relationship itself is still something two people have to choose, nurture, and walk through together.