For most of the 20th century, accepted knowledge in the world of neuroscience was that the adult brain did not grow new brain cells.  That could have changed in the 1960s, when scientists found brain cells growing in monkey brains, and then in human brains.  However, as science sometimes goes, rather than accepting the findings of the scientists who tried to publish their discovery of brain cell growth, called neurogenesis, the scientific community destroyed the reputation and careers of those who tried to bring their discovery to light.

After that, it took until the late 1990s before someone again brought forward evidence of neurogenesis.  Now, it is accepted that an area of the brain called the hippocampus grows new cells, and that cell growth occurs throughout the lifespan for those with healthy brains.

A study from 2019 that was published in Nature Medicine and summarized in Technology Network’s Neuroscience News and Research shows that there is some neurogenesis through at least the ninth decade of life.  This is true even in the brains of those with Alzheimer’s Disease, though the rate of growth is significantly diminished.  You can read the summary here and the study itself here.