Updated on October 6 at 12:26 p.m. ET

Jeanne Louise Calment spent all of her incredibly long life in Arles, France. She was born there in February 1875 and died there in August 1997. At the time of her death, she was the oldest person ever recorded—and she still is.

Perhaps she always will be.

For years, people have been saying that the first human who will live to 150 has already been born. That’s unlikely, say Jan Vijg, Xiao Dong, and Brandon Milholland, from the Albert Einstein College of Medicine. After looking at demographic data from the last century, they think that human lifespan has a hard ceiling at around 115 years. A few rare individuals like Calment may surpass that limit, if only slightly, but on average, our species will not.

That seems counter-intuitive. For centuries, our average life expectancy has been going up and up. Our maximum lifespan has too: Although claims of extreme age can be hard to verify, one reliable set of figures from Sweden showed that the very oldest people reached just 101 years in the 1860s but 108 years in the 1990s. “Demographers said that if there’s an end in sight, they couldn’t see it,” says Vijg, who led the new study. “When Calment died at 122, everyone said it’ll only be a matter of time before we have someone who’s 125 or 130. But after Calment, there was no one else. It was 115 … 115 … 115.”

To see if that perceived plateau was real, Dong, Milholland, and Vijg turned to two international databases on longevity and worked out the oldest individuals who died in any given year. They specifically looked at France, Japan, the United Kingdom, and the U.S.—the four countries with the most supercentenarians, people who live to 110 years or more.

The data were clear. Between the 1970s and early 1990s, our maximum age rose from around 110 to 115—and then stopped after 1995, shortly before Jeanne Calment died.  In fact, Vijg’s team calculated that in any given year, the odds that at least one person in the world will live past their 125th birthday are less than 1 in 10,000.

Despite sanitation, antibiotics, vaccines, and other medical advances, the oldest living people simply aren’t dying any later. They’re unlikely to either, regardless of calorie restriction, drugs like rapamycin, and all of our other efforts to slow the flow of sand through the hourglass. “In science, you never know,” says Vijg. “But I’ve not seen anything that I think would break through the ceiling.”

The ceiling is probably hardwired into our biology.  As we grow older, we slowly accumulate damage to our DNA and other molecules, which turns the intricate machinery of our cells into a creaky, dysfunctional mess. In most cases, that decline leads to diseases of old age, like cancer, heart disease, or Alzheimer’s. But if people live past their 80s or 90s, their odds of getting such illnesses actually start to fall—perhaps because they have protective genes. Supercentenarians don’t tend to die of major diseases—Jeanne Calment died of natural causes—and many of them are physically independent even at the end of their lives. But they still die, “simply because too many of their bodily functions fail,” says Vijg. “They can no longer continue to live.”

Why should life come to such a crashing halt? Imagine that you have an animal that doesn’t age. Despite its immortality, it can still starve, succumb to accidents, or fall to predators. Eventually, its luck always runs out. This imaginary creature should have a demography much like ours—lots of young individuals and fewer old ones. As such, evolution should favor genetic changes that offer advantages during early life—say, in growth or reproduction. By contrast, genetic changes that cause harm during later life would be ignored—they hardly matter when so few individuals reach those ages anyway. That’s why organisms age—evolution naturally and inexorably prioritizes the young in favor of the old.

But if early development and childhood experiences are so important to our future health, it’s notable that today’s centenarians were born in the 1900s. It might be that longevity records “haven’t yet seen the impact of the improved sanitation, healthcare, vaccinations, and hygiene advances that took place in the 1930s and later,” says Holly Brown-Borg from the University of North Dakota. Or perhaps, “our poor diets and lack of exercise have countered those gains.”

That’s unlikely to matter much, says Vijg. “Once you survive your childhood, you’re really more likely to survive over long periods of time. And there have been enormous advances in keeping older people alive much longer. We’ve continued to make progress in medical care and safety standards, and there are more and more people. You can’t explain the fact that there aren’t older people that Jeanne Clement except to say that we’ve hit a ceiling.”

We have pushed that ceiling upward for laboratory animals, like worms, flies, and rodents. But these creatures were specifically bred by scientists to grow fast and reproduce rapidly. Many of the techniques for extending their lives, from drugs to calorie restriction, probably work by simply slowing their artificially inflated growth.

Similar tricks might increase our healthspan, and raise our average life expectancy. But Vijg believes that the most we can hope for is to be very healthy for around 115 years, after which our bodies will just collapse.

“There’s no question that we have postponed aging,” adds Judith Campisi, from the Buck Institute for Research on Aging. “But to engineer an increase in maximum lifespan, we’ll probably have to modify so many genes that it won’t be possible within our lifespan—or even our grandchildren’s lifespan.”

After the paper was published, a few scientists on Twitter questioned the statistics behind it. Leonid Kruglyak, from the University of California, Los Angeles, suspected that the recent “plateau” is driven by a small number of outliers like Calment. If you remove them, it’s “not clear there’s any break in [the] upward trend beyond random fluctuations,” he said. He also questioned Vijg’s choice to analyze the change in maximum age before and after 1995, calling it an “arbitrary breakpoint”.

Vijg stands by the study. His team originally left Jeanne Calment out of the analysis; with or without her, the results are the same—no increase in maximum age after 1995. It didn’t matter which year he picked as the breakpoint either. “There simply is no significant increase from the early 1990s onwards,” he says. “I am sure that some people will argue that the upward trend may continue soon enough. While we agree that the data are noisy, which is to be expected the statistics are clear. Fortunately, all databases are public so everyone who wishes can do the math and disagree with us.”