Play store
Could lasting love have a mathematical formula? Researchers studying romantic relationships say the way feelings change over time may follow patterns that can be modeled with surprising precision.
Professor Laurent Pujo-Menjouet of the University of Lyon I and other researchers have developed mathematical models that treat romantic relationships as dynamical systems—systems whose conditions change over time in response to internal and external influences.
In his book Love! Valour! Equations!, Pujo-Menjouet brings together mathematics, psychology, literature, cinema and everyday life to explore how relationships evolve.
“There is no mysterious enchantment or magic potion,” he writes. “Is all hope lost then? Certainly not. That is precisely where everything becomes interesting.”
The mathematical study of relationships has roots in population science. Models originally developed to study animal populations—including Malthusian population models and predator-prey equations—have helped researchers understand how systems grow, decline and respond to changing conditions.
One such concept is the Allee effect, which describes a critical population threshold. When a population falls below that level, its chances of survival can decline sharply.
Researchers have applied a similar idea to romantic relationships, suggesting that couples may also have a critical level of emotional connection below which the relationship becomes increasingly difficult to sustain.
“We’re not trying to predict who you’ll fall in love with,” Pujo-Menjouet says. “We’re trying to understand why some couples remain stable despite life’s inevitable shocks while others slowly drift apart.”
The field has drawn on decades of mathematical and psychological research, including work by psychologist John Gottman, economist José Manuel Rey, physicist Sergio Rinaldi and mathematician Steven Strogatz.
Gottman’s research demonstrated that interactions between couples could be analyzed mathematically. By coding couples’ behavior and translating their interactions into data and graphs, researchers found that mathematical models could provide insights into relationship outcomes.
Later models introduced additional factors, including delayed emotional reactions. Such models recognize that people do not always respond immediately during disagreements and that taking time to reflect can either ease tension or allow conflict to intensify.
According to Pujo-Menjouet, one of the central ideas remains relatively simple: relationships may have a critical threshold of emotional strength needed to remain stable.
“If your feelings fall below this threshold and stay there, the mathematics predicts an inevitable decline toward separation,” he says.
The researchers also model everyday pressures such as stress, arguments and problems outside the relationship. Their findings suggest that the crucial factor is not whether couples face difficulties, but how well they recover from them.
“The important question isn’t whether couples argue,” Pujo-Menjouet says. “It’s whether they have enough resilience to return to equilibrium afterwards.”
The models identify three major forces affecting the long-term stability of a relationship: mutual attraction, the natural weakening of feelings over time, and each partner’s emotional response to the other.
Together, these factors determine how well a relationship can withstand stress and recover from conflict.
Pujo-Menjouet compares this resilience to The Three Little Pigs. Life will inevitably bring its “wolves”—including stress, illness, work, children and financial difficulties. Mathematics, he suggests, can help explain why some relationships are better equipped to withstand those pressures than others.