Friday is the day the math said we’d run out of room. In November 1960, the journal Science published a paper with one of the most memorable titles in scientific history: “Doomsday: Friday, 13 November, A.D. 2026.” Its authors calculated that at the rate humanity was growing, world population would shoot to infinity on that exact date. As UNILAD Tech noted, the date is now three days away, and the prediction is trending again.
We wrote about the paper when it was still 80 days out, in our first look at the doomsday equation. With the date almost here, we ran the formula ourselves for every decade since 1960 and compared it with real UN population data. The result is a neat lesson in how a model can fit the past perfectly and still be wildly wrong about the future.
The short version
- Physicist Heinz von Foerster and colleagues Patricia Mora and Lawrence Amiot fitted a curve to 2,000 years of population estimates.
- The curve hits infinity at year 2026.87, which lands on Friday, November 13, 2026. That’s also von Foerster’s birthday.
- For 2025, the formula predicts about 131 billion people. The UN puts the real figure at 8.2 billion.
- The model tracked reality well until the early 1970s, then broke when birth rates started falling.
- Nothing will happen on Friday. Population growth has been slowing for six decades.
The formula behind the headline
Most population models assume growth that is exponential at worst: a steady percentage each year, so the population doubles on a fixed schedule. Von Foerster’s team argued that wasn’t what the historical data showed. Growth wasn’t just fast, it was speeding up. The more people there were, the faster the growth rate itself climbed.
Their explanation was cooperation. More people meant more trade, more ideas and better technology, which let even more people survive. The authors called humanity a “coalition” that beats the limits other species run into. Fit that idea to roughly two dozen population estimates from year 0 to 1958, and you get a hyperbola:
N(t) = 1.79 × 1011 ÷ (2026.87 − t)0.99
N is world population, t is the year. As t approaches 2026.87, the bottom of the fraction approaches zero, and N heads to infinity.
That’s not an explosion in the everyday sense. It’s a mathematical singularity: the doubling time keeps shrinking until, on paper, it reaches zero. The authors were half joking. The paper’s most quoted line is “Our great-great-grandchildren will not starve to death. They will be squeezed to death.” Picking Friday the 13th, which also happened to be von Foerster’s 115th birthday, was part of the fun. Demographer Joel Cohen has said he doesn’t think von Foerster “was seriously trying to predict the future.”
Worth knowing: the paper’s own error bar on the date was plus or minus 5.5 years. Nobody quotes that part.
We ran the numbers
Here’s what the equation predicts at each decade, using mid-year values, next to the UN’s World Population Prospects estimates.
For the first decade or so, the fit is respectable. The formula slightly undershoots in 1960 and 1970, partly because the UN has since revised its historical estimates upward. Around the early 1990s, the two lines cross. After that, the formula takes off and reality doesn’t.
| Year | Formula says | Actual | Formula vs. reality |
|---|---|---|---|
| 2000 | 7.0 billion | 6.2 billion | 1.1x too high |
| 2010 | 11.2 billion | 7.0 billion | 1.6x too high |
| 2020 | 28.6 billion | 7.9 billion | 3.6x too high |
| 2025 | 131 billion | 8.2 billion | 16x too high |
| Mid-2026 | About 480 billion | About 8.3 billion | 58x too high |
| Nov 13, 2026 | Infinity | About 8.3 billion | You can’t divide by zero |
So what went wrong?
Nothing about the math. The problem was the assumption underneath it. The authors treated the growth pattern of the 1950s as a permanent law of human behavior. It turned out to be a phase.
Almost as soon as the paper came out, the trend flipped. World population growth peaked at about 2.3% a year in 1963, according to UN data compiled by Our World in Data. It has been falling ever since and is now under 1%. The global fertility rate dropped from 3.31 children per woman in 1990 to 2.25 in 2024, right around the level needed just to replace each generation.
Demographers call this the demographic transition. As child mortality falls, education spreads (especially for women), cities grow and contraception becomes available, families have fewer kids. It happened first in Europe and has now reached most of the world. Demographer Dean Spears put it bluntly in recent coverage: the doomsday premise was “based on a misunderstanding of where population growth comes from.” Historian Alan MacEachern notes that the global birth rate today is less than half of what it was in 1960.
Critics spotted the flaws back then, too. Letters to Science in 1961 called the paper ridiculous, and pointed out the obvious: a nine-month pregnancy puts a hard ceiling on how fast any population can grow, no matter how cooperative it is.
Where population is really headed
The UN’s latest projections, from its 2024 World Population Prospects, show something closer to the opposite of a doomsday spike. World population is expected to keep rising slowly to a peak of about 10.3 billion in the mid-2080s, then start to decline, reaching about 10.2 billion by 2100.
UC Santa Barbara economist Javier Birchenall made this point with a wink in an essay in Science last month. He argued von Foerster’s team made a “sampling error” by treating 1960 conditions as permanent, then built his own mock doomsday by projecting Japan’s shrinking population onto the entire world. Same flaw, opposite direction.
If you want real risks to worry about, there are better candidates than a curve from 1960. The Lancet recently ranked the biggest threats to human health this century, and we went through what made the list and what topped it.
The takeaway
A formula can match every data point you have and still fail the moment the underlying behavior changes. That’s true for population curves, stock charts and AI forecasts alike. Von Foerster’s paper is a great reminder to ask not just “does this fit?” but “why would this keep going?”
On Friday, the Complexity Science Hub in Vienna is even hosting a conference on the sense and nonsense of end-of-the-world predictions, timed to the date. Von Foerster, who was born in Vienna and died in 2002, would probably have enjoyed that. His equation never came true, but more than six decades later, it’s still getting people to talk about the math of the future.
About this article: GeekBlog covers U.S. technology news, AI, phones, smartwatches and gaming. Every story is written and checked under our Editorial Policy. Spotted a mistake or have a story tip? Contact our editors.
