There have been a couple of recent movies in a sci-fi or thriller genre on the theme of overpopulation (spoiler alert!). Examples are Inferno, based on the Dan Brown book, and of all things Marvel's Avengers: Infinity War. In both, the villain (hero?) has decided that overpopulation is the cause of the world's (read galaxy's) ills, and the solution is to kill off half of all living people (read intelligent life forms). In one movie, the solution is a novel bioengineered deadly virus, in the other it's a gauntlet powered by remnant energy from the Big Bang (or something like that, it's left a bit vague).

Almost needless to say, in the absence of any additional actions both of these schemes are completely pointless. Populations expanding by exponential growth will inevitably recover to their previous size in the absence of any new checks, and potentially very quickly. If one were to kill off half of all intelligent life in the universe, and the ones left just had four kids each (for species with a mere two genders), then in a generation things would be right back to where they were before. I've oversimplified the numbers a bit, not being an epidemiologist I'm not sure what the exact number of extra kids would have to be, but it's small. As a real world example, after many years of flat budgets, the NIH in the US doubled its total research funding during the 1990's, after which it once again became fairly flat. After a short period where success rates of new grants rose dramatically, that too levelled off as universities hired more researchers. Today the success rate for new research proposals at the NIH is low again, pretty much back where it was before the budget doubled. The reason is that the size of the research community also tends to grow exponentially (though with a fairly small absolute exponent). In such a situation, in order for the new grant proposal success rate to stay high, the total budget also has to grow exponenentially, forever as in every single year. That is completely unrealistic in today's economy.

The only way to prevent inevitable human overpopulation is to either 1) keep killing off a big chunk of the population every generation by war, famine, disease, etc, or 2) reduce the birth rate to replacement value or less. In fact, with scenario 2 you don't have to actively kill off anyone, since we have a natural mortality rate. By managing the total birth rate, one can achieve any desired absolute population, as quickly or slowly as you want, and do so stably and with minimal violence.

Unfortunately, such a scenario is fairly unlikely, since humans are no better at self-restricting their population growth rate than any other species. The sad part, and the way we are in fact special, is that we are capable of understanding this. No other species as far as we know consciously restricts its population, although all species' birth rates are regulated in some way according to their environment. Indeed, there are places in the world where stable human populations are the norm, or have become so. In industrialized countries such as in Japan or Europe, this actually creates a problem since our capitalist economies demand constant growth, ultimately driven by population size. A  stable population requires a completely different economic model at least to avoid widespread poverty. That too seems pretty unlikely at the moment, although there are lots of proposals of how such a truly sustainable economy could work. I can only hope that some fairly severe shocks to the system will wake enough people up that they will entertain such counter-evolutionary, yet long term necessary, alternatives.