The brain, before your born, in GW25 (gestational week 25) has finished growing all the neurons you're basically [we can talk about this later perhaps] going to have for the rest of your life. At GW25 current estimates say you have ~86 billion neurons. Now the timing for this next part is a bit unsure but your body doesn't need anywhere close to 86 billion neurons, so at some point as early as early adulthood you start to lose 85,000 neurons per day pretty steadily until you die. Now neurons are not the end all be all because connections are potentially what really matter but that is to say that the neurons that you have after GW25 are the neurons you basically have. Now going onto synaptic connections where things start to matter more. Now synapses form and then get pruned all the time its natural. But the rate of formation and the rate of pruning is not the same at all times of life. Now from a raw number of synapse scale we see a tipping point at around 16-26 years old (debated hence the big range) where the number of synapses start to go down, indicating that the rate of pruning is now outpacing the rate of formation. [It does seem however that the dysfunction of the rate of pruning i.e. not enough ends up with consequences like schizo or asd {autism}]. There is another factoid that the rate of decline seems to stay relatively stable until you hit ~60 and then synapse related decline becomes much more noticeable and we start to think of synapse loss as exponential.
Now about new neurons after GW25 is a whole topic in of itself... heavily debated but I won't get into that history, the most accepted viewpoint is that it does exist in the hippocampus [other regions as well] (really cool work with c14 carbon dating from atomic bomb {2010} and perhaps less cool new sequencing methods give evidence {2025/2026}). Note estimates of how many are born are comparatively low-ish, 500-1000 neurons per day.
That begs another question however which is why and what do they do? Final interesting part is that when you stop the mouse hippocampus neurons from dividing, [unethical to do in humans :( ] distinct representations of experiences start to look similar and overlap. I also know if you ablate neurogenesis in mouse nasal cortex I think mice lose the ability to form new sensory sensations all together.
Disclaimer, the evidence for function of new born neurons is actually pretty low only a few studies have tried this so its no where close to accepted and thus far far from textbook standard so take it as you will.