From The 1960 Doomsday Hypothesis That Should Have Made 2026 Diverge To Infinity, To A Nonlinear Equation That Reconciles 12,000 Years Of Human History. The New Mathematical Framework Treats Population As A Switchable System That Can Grow, Saturate, Or Collapse
According to ProPakistani, citing the original research published via Phys.org and authored by the late Kostya Trachenko of Queen Mary University of London with his collaborator, a new open-access study proposes a surprisingly simple nonlinear mathematical equation that unifies 12,000 years of human population growth and points to stark possible futures if global environmental crises intensify.
The headline scenario produces a rapid contraction pathway in which the global population could roughly halve by around 2064; a swing of more than four billion people from current levels.
This is not a forecast. The authors are explicit on that point. The baseline projection indicates no imminent global collapse. What the mathematical model does is open a sensitivity window; a mathematical experiment showing how abrupt systemic stress could reshape the world’s population if Earth’s carrying capacity is sharply reduced through climate change, pandemics, or resource constraints.
The 1960 anchor matters. The study revisits one of the most famous predictions in population science: the “doomsday” hypothesis advanced in 1960 by Heinz von Foerster and colleagues, who mathematically extrapolated that the global population would diverge toward infinity around 2026.
Humanity avoided that trajectory because fertility rates declined globally through the second half of the 20th century. We are living through the year that hypothesis identified, and the world holds roughly 8.3 billion people; not infinity, but a meaningful test of how far an extrapolation can be wrong when the underlying dynamics shift.
The new mathematical study argues that the same underlying mathematics of runaway behaviour can reappear in the opposite direction under different conditions.
The empirical context makes this more than a thought experiment. Global fertility is already collapsing on a timeline most observers underestimate. The UN’s 2024 World Population Prospects shows the global fertility rate at 2.25 live births per woman, projected to fall below the 2.1 replacement threshold around 2050.
The IMF estimates the world population will peak at approximately 10.3 billion in 2084 before declining gradually thereafter. The Lancet’s 2024 study by the Institute for Health Metrics and Evaluation projects that by 2050, 155 of 204 countries will have birth rates below replacement.
By 2100, that figure climbs to 198 countries; 97% of the world’s population. In thirteen countries, including South Korea, Bosnia, and Bhutan, women will average less than one child each.
The collapse is no longer a tail-risk scenario. It is the central-case forecast for nearly every developed economy.
The new model’s contribution is mathematical, not predictive. What Trachenko’s framework provides is a unified equation that fits all major phases of human history; the slow Holocene rise, the agricultural-revolution acceleration, the industrial-era explosion, and the recent saturation.
By treating population as a complex nonlinear system, the model demonstrates that the trajectory can switch between three stable regimes: continued growth, plateau saturation, or rapid collapse. Which regime takes hold depends on the relationship between human population pressure and Earth’s carrying capacity.
Reduce carrying capacity sharply enough through ecological breakdown, sustained pandemic mortality, or compound resource scarcity and the system flips into contraction faster than any linear extrapolation would predict.
Why halving by 2064 is mathematically plausible even if politically unimaginable. The Black Death, the only previous documented global population decline, reduced the world’s headcount from roughly 400 million to 350 million in the mid-1300s; a 12.5% drop over a few decades. The 2064 scenario in the new study is a 50% decline in 40 years. That is not a Black Death repeat.
It is roughly four times the proportional severity, compressed into less time. The scenario requires multiple concurrent stressors: climate-driven agricultural failure across the mid-latitude breadbaskets, multiple pandemics overlapping with reduced healthcare capacity, fertility collapse continuing below 1.0 in major economies, and migration absorption failures in receiving countries. No single one of these is sufficient. The combination is.
The pro-natalist response is already organising. The American Enterprise Institute has flagged the global fertility crisis as worse than mainstream estimates suggest. If global fertility converges to 1.2; the average for East Asia today, the global population reaches 1 billion by 2240 and just 10 million by 2500.
Figures like Elon Musk have publicly argued that civilisation will disappear unless birth rates change. South Korea, Japan, Hungary, and now China are running policy experiments; cash payments, housing subsidies, tax breaks designed to lift fertility. The results so far are modest at best. The fertility-decline dynamic has proven remarkably resistant to financial incentives.
The deeper challenge is conceptual. For two hundred years, the framing of demographic anxiety has been overpopulation. Malthus, the Club of Rome, the limits-to-growth debate, the population-bomb literature. The infrastructure of governance, urban planning, food production, healthcare and education has been built around the assumption that the human headcount keeps rising.
The Trachenko model is one of many recent research outputs reminding policymakers that the assumption may already be inverted. The pension systems of every developed economy depend on a worker-to-retiree ratio that the projected demographics make impossible. The investment thesis behind real estate in most ageing societies looks completely different if the population is contracting rather than expanding.
What the new model adds to the existing literature. The IHME, IMF and UN projections all assume a smooth glide path; population peaks gradually, then declines gradually. Trachenko’s contribution is to argue that the underlying dynamics may not be smooth.
A complex nonlinear system can switch states quickly. A small additional stressor can move the trajectory from saturation to collapse in a non-linear way that the smooth-glide models cannot capture. This is not a prediction that collapse will happen. It is a warning that the system is more brittle than the linear assumptions imply.
The verdict. Four billion fewer people by 2064 is a worst-case scenario, not a forecast. But the difference between worst-case scenario and central case is narrower than the public conversation acknowledges. Global fertility has already fallen below replacement. The drivers of carrying-capacity reduction; climate, resource depletion, geopolitical fragmentation are all moving in the wrong direction.
The mathematics shows a switchable system. The policy systems show no readiness for the switch. This study will not settle the demographic debate. It will sharpen it.
To check out our previous coverage on global demographics, climate, and long-term economic shifts, read our articles here.
