French mathematics professor Laurent Pujo-Menjouet has released a book featuring differential equations designed to measure and predict the trajectory of romantic relationships.
Can the trajectory of a relationship be reduced to an equation? That is the premise put forward by French mathematics professor Laurent Pujo-Menjouet in his new book, Love! Valour! Equations! Mathematics of the Couple. Rather than treating romance as entirely beyond calculation, the framework invites readers to view human relationships through the simplified lens of mathematical modeling.
At the center of the model is a differential equation tracking the rate of change in romantic feelings over time. The formula incorporates several distinct variables representing the mechanics of long-term partnership. On one side sits erosion
, accounting for the inevitable habituation that settles into pairs over the years. Other variables capture random life shocks—such as a job loss, financial trouble, a career promotion, having a child, a bereavement, or infidelity—alongside the partner’s behavioral reaction, which might manifest as an apology or an affectionate gesture.
Inside the Mathematics of Romance and Critical Thresholds
The system also relies on a critical threshold value. If emotional connection drops below this specific tipping point, the model projects that the feeling will inevitably slide to zero, resulting in a separation. Pujo-Menjouet argues that the academic community possesses powerful theoretical tools that should be brought out of the laboratory and applied to human behavior, much like mathematics aided physics, chemistry, and biology.
In the book’s preface, University of British Columbia mathematics professor Rebecca Tyson notes that while such models can yield valuable insights, human social behavior remains intensely complex. No single mathematical framework will ever fully capture it.
We have extremely powerful theoretical tools at our disposal. Laurent Pujo-Menjouet, mathematics professor
Where Behavioral Psychology Pushes Back
Specialists in family dynamics and clinical psychology argue that individual relationship outcomes resist strict prediction. Guy Bodenmann, a professor of clinical psychology at the University of Zurich who researches couples and families, points out that psychological research can identify general patterns for maintaining a relationship, but forecasting an individual trajectory remains out of reach.
Bodenmann highlights that roughly one-quarter of couples who ultimately divorce report being satisfied with their relationship beforehand, challenging the assumption that a measurable buildup of distress always precedes a split. Separations depend just as much on available alternatives, biographical factors, and specific tipping points.
Demographic context plays a parallel role. Marriages tend to dissolve less frequently in rural areas compared to cities, among couples sharing similar educational backgrounds, and among religious partners.
The Practical Viewpoint From Psychotherapeutic Practice
Practicing clinicians offer a different perspective on how feelings evolve in real time. David Wilchfort, a specialist in psychotherapeutic medicine in Munich, expressed skepticism toward the idea of a predictable, steady decline in affection.
In my practical experience with thousands of couples, I do not experience a consistent, predictable depletion of feelings. In reality, feelings change from moment to moment. David Wilchfort, psychotherapeutic medicine specialist in Munich
Wilchfort adds that emotions can pivot from icy distance to close connection within a single session. The survival of a relationship depends fundamentally on the inner attitude toward the partner—specifically, whether both individuals maintain a core conviction that the other’s well-being matters.
Other practitioners view behavioral indicators differently. Psychotherapist Wolfgang Krüger adopts a more receptive stance toward structural approaches in couple research, pointing to the work of John and Julie Gottman on relationship stability. Krüger relies on a simpler behavioral litmus test in his own practice, asking couples whether and how they still kiss, which he considers a reliable gauge of lingering intimacy.
Between Structural Forces and Unpredictable Realities
The debate surrounding mathematical relationship models underscores a permanent tension between statistical generalization and human unpredictability. While population researchers examine structural anchors like education, religion, and financial dependency to explain why some partnerships endure, therapists observe that daily emotional currents shift too rapidly for differential equations to capture.
As these formulas enter public discourse, researchers on both sides agree that while broad patterns can be mapped, the inner mechanics of any single relationship continue to defy rigid formulas.
