What does the way certain amorphous materials evolve at the atomic level have in common with the growth of the human population? At first glance, nothing. However, a physicist from the University of Milan and his late colleague from Queen Mary University of London maintain that the same mathematical equation can be applied both to the study of certain amorphous materials and to the demographic evolution of humanity. And, according to their model, that opens the door to scenarios that invite reflection.

And the issue is not minor. As humanity continues to grow and consume resources at an ever-increasing rate, the fear of an eventual global demographic collapse remains latent for many. What would happen if the Earth were no longer able to support the current population?

A mathematical model for 12,000 years of demographic history

Its main strength is versatility. With a single parameter, the model can describe different stages of demographic evolution – from long periods of slow expansion to much more intense phases of acceleration – without needing to modify the equation. This differentiates it from traditional demographic approaches, which usually use different exponential or logistic models to represent each behavior.

The model also has an unexpected origin. Alessio Zaccone, lead author of the work, originally developed this equation together with Kostya Trachenko to study how certain amorphous materials evolve at the atomic level. That the same mathematical structures serve to model human societies is, to say the least, disconcerting.

Possible extreme futures

But one of the most striking aspects of the study is not in its ability to reconstruct the past, but in the projections it raises about the future.

In one of the most extreme scenarios analyzed, a global crisis could drastically reduce the number of people the planet could stably support. In that case, if the Earth could only support about 2 billion people long-term, the model estimates that the world's population could be reduced by about half by 2064.

According to Gizmodo, this would mean going from the expected 8,000 to 10,000 million inhabitants to just between 4,000 and 5,000 million in just over four decades.

Hypothetical scenarios mentioned by the authors include a nuclear winter, a major pandemic, extreme climate collapse or, perhaps more possible, the simultaneous combination of several global crises.

Still, Zaccone clarifies that the study should not be interpreted as an apocalyptic prediction. According to the researcher, this is not an imminent or especially probable scenario. “The current trajectory remains relatively stable and does not imply an imminent collapse,” he explains in a statement.

The model also contemplates the opposite scenario: an accelerated demographic expansion that would end up becoming mathematically unsustainable. According to that simulation, global population growth would reach that threshold around 2078.

The study also reviews the famous prediction made in 1960 by Heinz von Foerster, who calculated that the human population would head towards a demographic acceleration without mathematical limit by 2026, a trajectory that ultimately did not materialize as fertility rates began to decline in much of the world. According to Zaccone, the mathematical dynamics behind that extreme growth could reappear under certain conditions.

A tool, not a prophecy

According to the statement, the model was contrasted with empirical data from different periods and managed to successfully reproduce both the “compressed exponential” phases – such as the industrial boom – and the slower “stretched exponential” growth that has characterized global demographics since approximately 1970.

Even so, Zaccone insisted, both in the official statement and in statements reported by Newsweek, that the model "is not intended to predict the future." Their projections should be understood more as illustrative scenarios than as concrete forecasts. "Relatively small changes in the parameters of the equation can lead to drastically different scenarios," the researcher explained to Newsweek.

Falling birth rate: the global demographic map

The study also arrives at a time when the global demographic panorama continues to be marked by strong contrasts. While some countries are registering a sharp drop in birth rates, others are experiencing the opposite phenomenon. Newsweek highlights that fertility in the United States fell to 1.6 children per woman, below the level considered necessary to keep the population stable. China, for its part, recorded its lowest number of births in decades in 2025. And Russia, which has been experiencing a sharp demographic decline for years, has seen this trend worsen since the start of the war in Ukraine.

In contrast, sub-Saharan Africa is heading towards strong population growth. According to United Nations estimates, the region's population could grow by nearly 80% by 2054 and exceed 2.2 billion inhabitants, driven by countries such as Niger, Chad or the Democratic Republic of the Congo.

In this context, perhaps the true value of the study lies not in announcing catastrophes or in trying to guess what the fate of humanity will be, but in remembering that demographic dynamics are much more fragile, complex and non-linear than we usually assume. And that, in a world crossed by climate crises, geopolitical tensions and increasingly interconnected health threats, understanding this complexity requires mathematical tools to match.