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Published in May 2026 in the journal Chaos, Solitons & Fractals, the model by physicists Alessio Zaccone and Kostya Trachenko is not a prediction but an extreme illustrative scenario. The official UN projection points to world population growth until a peak in the 2080s, with no collapse in sight.
A study published on May 22, 2026, in the scientific journal Chaos, Solitons & Fractals placed an equation from materials physics at the center of a debate about the future of the world population. The research was authored by physicist Alessio Zaccone, from the Department of Physics at the University of Milan, Italy, and his late colleague Kostya Trachenko, from Queen Mary University of London, UK. The authors showed that the same equation, originally used to describe the behavior of glass and other amorphous solids, can reproduce human growth over approximately 12,000 years and, in an extreme scenario, points to a halving around 2064.
Zaccone himself emphasizes that the result is not a prediction, but an illustrative mathematical scenario. The calculation starts from a deliberately pessimistic hypothesis, that the Earth’s carrying capacity, i.e., the number of people the planet could sustainably support, suddenly drops to about 2 billion. Under this premise, the world population would decrease from the approximately 8 billion predicted for the period to near 4 billion in just over four decades, according to the model described by the researchers on the Phys.org portal and in interviews with the international press.
A glass equation that describes 12 thousand years of history
Zaccone and Trachenko developed the equation to study how disordered materials, such as glass and amorphous solids, react to stress and relax over time within the physics of condensed matter.
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These materials have a peculiar behavior, as they resist extreme conditions and, in certain seemingly less severe situations, can break entirely.
It was this same mathematical format that the two physicists decided to apply to the human population curve.
Named by some researchers as the Trachenko-Zaccone equation, the formula is a nonlinear feedback model that describes the growth rate with a single parameter.
According to the study, it reproduces with good adherence both the phases of accelerated expansion, such as the population explosion of the industrial era, and the slower growth observed since around 1970.
More than that, it encompasses as particular cases classical demographic regimes, including Thomas Malthus’s exponential growth, Pierre Verhulst’s logistic growth, and the so-called doomsday formula by Heinz von Foerster.
The 2064 Scenario and What It Really Says
The most provocative part of the work lies in the future projections, and it is also the most delicate.
When fed with the hypothesis of a sudden drop in carrying capacity to 2 billion people, the equation returns a trajectory of rapid decline, with the world population halving around 2064.
In absolute numbers, this would mean retreating from the approximately 8 billion inhabitants expected for the period to something close to 4 billion.
Depending on the base projection adopted, Gizmodo magazine reported that the drop could range from 8 to 10 billion to 4 to 5 billion.
What would trigger this collapse, within the model, would be a large-scale global shock, such as a severe pandemic, a widespread war, or a climate and resource collapse.
Even so, Zaccone repeats in all interviews that this is not the most likely path.
In a statement reproduced by the press, the physicist stated that the current trajectory remains relatively stable and does not indicate imminent collapse, and that the 2064 scenario serves to show how sensitive population dynamics can be to abrupt changes, not to mark a date on the calendar.
The Legacy of von Foerster’s Doomsday Formula
The study also revisits a famous and failed prediction of mathematical demography.
In 1960, the scientist Heinz von Foerster published a calculation according to which the human population would tend towards infinity around 2026, in an unlimited acceleration that became known as the doomsday formula.
The projection did not materialize, precisely because fertility rates began to fall in much of the world in the following decades.
However, for Zaccone, the mathematics behind that explosive growth has not disappeared completely.
The researcher argues that this type of dynamic could reappear under certain conditions, and that simple and non-linear models help to study precisely the points where the relationship between humanity and the environment can change regime abruptly.
In this sense, the equation would function less as a crystal ball and more as a thermometer of the system’s fragility.
What demographers project and where the model finds limits
The main official demographic projections paint a very different picture from the collapse of 2064.
In the World Population Prospects 2024 report, released in July of that year, the United Nations estimated that the world population should grow from the 8.2 billion recorded in 2024 to a peak of about 10.3 billion in the mid-2080s, gently receding to around 10.2 billion by 2100. According to the UN, the probability of the peak occurring still in this century is about 80%.
Other respected groups also work with gradual decline, not abrupt fall.
The Institute for Health Metrics and Evaluation, from the University of Washington, in a study published in The Lancet in 2020, projected a peak of about 9.7 billion people precisely in 2064, followed by a decline to around 8.8 billion by 2100.
The demographer Wolfgang Lutz and the Wittgenstein Centre, in Austria, arrive at lower and earlier peak scenarios based on education and urbanization trends.
The central difference is in the method, as these models detail age structure, fertility, mortality, and migration, while the equation of Zaccone and Trachenko condenses everything into a single statistical physics parameter.
The author himself acknowledges this limitation.
Zaccone states that the equation was not created for demography and that small variations in the parameters can lead to radically different results, which makes the model powerful as a long-term analysis tool, but fragile as an instrument for predicting dates.
That is why he insists on calling the result a scenario, not a forecast.
In the end, the most solid contribution of the work may not lie in the year 2064, but in the unexpected bridge between glass physics and the fate of the world population.
The idea that the same equation that describes the breaking of an amorphous material can describe the vulnerability of an entire civilization is, at the same time, elegant and uncomfortable.
It does not announce the end, but reminds us that complex and interconnected systems can change state faster than we imagine when subjected to simultaneous shocks.
Leave your opinion in the comments: do you think that using an equation created to study glass as a mirror of humanity’s future helps to see real risks, or does it just amplify unlikely scenarios? Do you believe that physics models have something to teach demography? Comment with respect for different views and share this article with those who love science and great questions about the future.
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