Having more kids might be the most important way to improve science
The problem is that depopulation is a self-reinforcing cycle. Many "developed" countries have made unsustainable commitments to pension and healthcare systems that depended on tax revenue from a growing workforce and economy. As the age dependency ratio rises and expense of maintaining these systems balloons, the only choice is to 1) Cut the benefits or 2) Raise taxes on the young. The latter seems to be preferred.
But the latter "solution" only adds to the burden on the young and discourages more children, reinforcing the cycle. At Risk & Progress, I have repeatedly argued that depopulation is the single greatest threat to humanity this century. It threatens to dampen growth, dampen specialization of labor, as well as weaken innovation capacity.
There do not seem to be any good solutions as pro-fertility policies I have studied this far have only had minor effects (though I will be exploring some more in another essay). Ironically, this comes at a time where we are also getting close to AI. Perhaps, if AI is aligned and safe, AI could mitigate the effects of global stagnation.
I am not disagreeing with you, but I would say that it is less about absolute population, and more about the population living in cities. Rural areas rarely make major contributions to science or technological innovation. The people in rural areas are too spread out geographically, and they focus their labor on getting enough food to eat. City dwellers have the time to focus on solving other problems, and the geographical concentration to share ideas and learn from others.
This matters because for virtually all of human history, few people lived in cities. If present trends continue, we will keep getting more urbanized, which might counteract lower populations.
China's population has been stable for 40 years, but real wages have doubled every decade and are on track to redouble by 2030.
India's population has doubled in that time, but it has produced nothing of interest.
If a nation has strong property rights in particular and the rule of law in general, and if that nation embraces freedom, then that nation's economy will grow. So as the world population shrinks, to the extent to which more people move to places with these three characteristics, the world economy will continue to grow.
This seems both a lilttle too focused on the long run and overly simplistic.
Population does not matter if none of the population performs research in the pure and applied sciences. Progress also halts if the culture somehow makes ideas permanently rival and/or excludable, as the Disney corporation, among many others, has attempted and wants to do more of. Culture should not be neglected.
In the short run (the next two centuries, say), there are great gains to be had merely from bringing people into the workforce who are currently excluded from it. I watched a youtube mini-documentary yesterday, that pointed out that 75% of Indian women are excluded from the workforce for cultural reasons. Approximately 400 million people. Many of these women are highly educated, with tertiary degrees and even graduate qualifications. In other parts of the world, the local culture cannot even maintain basic infrastructure such as stormwater control, water supply and sanitary waste disposal networks, or primary schools and basic healthcare clinics.
If you want maximum progress, these problems seem like the ones to work on. The long run is a chain of short runs.