Researchers at Columbia University examined whole hippocampi donated from people who had died between the ages of 14 and 79, looking for the specific cell types that mark ongoing neuron production.
The team found similar numbers of immature neurons and neural progenitor cells across the full age range, along with stable volume in the memory-related dentate gyrus region, though older brains showed less new blood vessel growth and a smaller pool of quiescent progenitor cells in part of the region.
The result suggested that healthy aging alone does not shut down neuron production, even if some supporting processes slow down. The conclusion is contested: a separate 2018 study in Nature, using different tissue preparation and markers, found no evidence of new neurons past adolescence, and researchers in the field still disagree about which methods best capture what is actually happening in living human brains.

Read the original study
Boldrini et al., Cell Stem Cell, 2018 · doi.org/10.1016/j.stem.2018.03.015
Two careful studies, two different answers.
Source
- Boldrini, M., Fulmore, C. A., Tartt, A. N., Simeon, L. R., Pavlova, I., Poposka, V., Rosoklija, G. B., Stankov, A., Arango, V., Dwork, A. J., Hen, R., & Mann, J. J. (2018). Human Hippocampal Neurogenesis Persists throughout Aging. Cell Stem Cell, 22(4), 589–599.e5. https://doi.org/10.1016/j.stem.2018.03.015