Researchers at the Albert Einstein College of Medicine tested that assumption against global demographic records instead of intuition. They tracked both the rate of survival improvement at the oldest ages and the record age at death itself.
The team found that gains in survival slow sharply after age 100, and that the age of the world's oldest verified person, 122 years at death, has not been broken since the 1990s despite a rapidly growing population of centenarians. The yearly record age at death plateaued near 115, and their model put the odds of anyone passing 125 in a given year below 1 in 10,000.
The finding challenged the view that medical and technological progress would keep pushing the maximum lifespan upward indefinitely. A 2018 paper in Science disputed the conclusion, arguing the data are also consistent with mortality risk leveling off rather than hitting a hard wall, and the debate over a fixed ceiling is still unresolved. No one has yet verified a longer lifespan than the 1997 record.

Read the original study
Dong, Milholland and Vijg, Nature, 2016 · doi.org/10.1038/nature19793
A record set in 1997, still unbroken.
Source
- Dong, X., Milholland, B., & Vijg, J. (2016). Evidence for a limit to human lifespan. Nature, 538(7624), 257–259. https://doi.org/10.1038/nature19793