People keep making new brain cells throughout their lives (well at least until the age of 97), according to a study on human brains.
The idea has been fiercely debated, and it used to be thought we were born with all the brain cells we will ever have.
The researchers at the University of Madrid also showed that the number of new brain cells tailed off with age.
And it falls dramatically in the early stages of Alzheimer's disease - giving new ideas for treating the dementia.
Most of our neurons - brain cells that send electrical signals - are indeed in place by the time we are born.
Studies on other mammals have found new brains cells forming later in life, but the extent of "neurogenesis" in the human brain is still a source of debate.
The study, published in Nature Medicine, looked at the brains of 58 deceased people who were aged between 43 and 97.
The focus was on the hippocampus - a part of the brain involved in memory and emotion. It is the part of the brain that you need, to remember where you parked the car.
Neurons do not emerge in the brain fully formed, but have to go through a process of growing and maturing.
The researchers were able to spot immature or "new" neurons in the brains that they examined.
In healthy brains there was a "slight decrease" in the amount of this neurogenesis with age.
Researcher Dr Maria Llorens-Martin told BBC News: "I believe we would be generating new neurons as long as we need to learn new things.
"And that occurs during every single second of our life."
But there was a different story in the brains from Alzheimer's patients.
The number of new neurons forming fell from 30,000 per millimetre to 20,000 per millimetre in people at the beginning of Alzheimer's.
Dr Llorens-Martin said: "That's a 30% reduction in the very first stage of the disease.
"It's very surprising for us, it's even before the accumulation of amyloid beta [a hallmark of Alzheimer's] and probably before symptoms, it's very early."
Alzheimer's disease remains untreatable, but the main focus of research has been targeting clumps of amyloid beta in the brain.
However, even last week more trials using this approach have failed and the latest study suggests there may be something happening even earlier in the course of the disease.
Dr Llorens-Martin says understanding why there is a decrease in neurogenesis could lead to new treatments in both Alzheimer's and normal ageing.
But she says the next stage of research will probably require looking in the brains of people while they are still alive, to see what is happening over time.
Dr Rosa Sancho, the head of research at Alzheimer's Research UK, said: "While we start losing nerve cells in early adulthood, this research shows that we can continue to produce new ones even into our 90s.
"Alzheimer's radically accelerates the rate at which we lose nerve cells and this research provides convincing evidence that it also limits the creation of new nerve cells.
"Larger studies will need to confirm these findings and explore whether they could pave the way for an early test to flag those most at risk of the disease."
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