Do we have a limited amount of neurons? Do they regenerate or does our brain make more?

There are a lot of archaic and inappropriate answers here, please disregard them. The only the one that is correct by current scientific understanding as of 2019, provided by Xeno Rasmusson, is nice enough to point out that the idea of what’s valid about this topic is something that changes over time and with more knowledge and research. My own answer below will be outdated, eventually, by a better answer.

I’ll skip the lesson on how the human brain forms in the first place and just start with what happens when it’s growing. Neurogenesis, the process by which progenitor neural stem cells migrate from the brain’s ventricular zone to various locations in the brain and mature as neurons in a network, is not just a rare or one-time event. There’s a massive spike in neurogenesis during the first few years of life, which is fairly apparent by the matter in how fast infants, of any species, cognitively mature. The rate of human neurogenesis in the brain slows considerably after infancy, but otherwise continues on for another three decades. The process is currently thought to slow down to a near-stop between ages 25–30, after which neurogenesis becomes something of a more specialized function in the brain that replaces very specific cells at a much slower rate of production than in any other stage. Current research on that with humans and other animals points to key anatomical regions, the sub ventricular zone and hippocampus, where this system remains functional late in life. This seems to continue even until death at a very old age, never stopping unless the system is affected by some kind of brain disease or injury.

All along the way, brain cells are dying as well. A young brain that is generating neurons in the millions-per-day amount is also losing a handful per day. The number goes up a lot, and switches out with neurogenesis as the dominant behaviour of cells in this conversation at around the same key age: 25–30 years old. Oddly enough, that’s about the natural human life span, at least until the modern era. A 60-year old might be losing millions of neurons per day and growing just a few hundred, but that isn’t always a bad thing.

A note worth making is that while new neurons do come about in great numbers during one’s lifetime, they are just that, new neurons. They migrate into an existing and very complicated network, merging into it in a new way. Neurons, complete with their particular network connections to other cells, do not replicate themselves as other types of cells do. Once dead, the place that that neuron occupied in the network is forever changed. As a sci-fi example, if your current brain-load of neurons all died instantly and was somehow magically replenished with new neurons that followed the process of neurogenesis, you would no longer be you. You would be a new-born baby in an old body.

A second note to make, then, is that the number of neurons in the brain is, for the most part, irrelevant for humans. 10 or 300 billion, doesn’t necessarily make a lot of behavioural difference. We couldn’t suffice too well with all of 50, but no complex organism could as such. It’s the sophistication in the network interactions of mature neurons that drives most brain function and cognitive maturation, not the ability to regenerate cells. Having a tremendous number of brain cells doesn’t compare to having a well-functioning network using far fewer cells. Hence, children can’t usually outsmart adults.

Reference: Kits Arriet