Take a fixed number of humans with a fixed intelligence (both average and outliers) then let mathematics advance. It will advance to the point that there is a vanishingly small number of people who can even understand the state of the art
This ignores the possibility of advances in the teaching of math (or physics, or any other discipline). If improved teaching methods lower the level of intelligence required to reach a given level of knowledge, then a field can advance considerably.
Not to mention that the human population has been growing, and average intelligence has been increasing.
Finally, there’s specialization. It doesn’t take much intelligence to know everything that was known about genetics when Darwin was alive, but probably nobody is smart enough to know everything that was known about it in 2000. But there have still been make advances since then thanks to people specialized in subfields like DNA sequencing.
OK advances in teaching the highest level of physics/math needed for string theory is a big IF. Do you have evidence that is actually happening? I know of two people who tried to learn it and just found it too hard, don’t think a better teacher or materials would have helped. The evidence is mixed but personal accounts certainly suggest that only a very small number of people could get to such a high level and improved teaching probably wouldn’t help much. When we are talking about such extreme skills, people have their plateau or maximum ability level which is mostly fixed.
The human population growing just pushes us along the asymptote faster, rather than changing it.
Any specialization advantage is already tapped out with string theory and similar. My worldview definitely does not apply to advances in a field like biology as there is lots of experimental data, the tools are improving etc. I would expect advances there without any obvious plateau yet.
This ignores the possibility of advances in the teaching of math (or physics, or any other discipline). If improved teaching methods lower the level of intelligence required to reach a given level of knowledge, then a field can advance considerably.
Not to mention that the human population has been growing, and average intelligence has been increasing.
Finally, there’s specialization. It doesn’t take much intelligence to know everything that was known about genetics when Darwin was alive, but probably nobody is smart enough to know everything that was known about it in 2000. But there have still been make advances since then thanks to people specialized in subfields like DNA sequencing.
OK advances in teaching the highest level of physics/math needed for string theory is a big IF. Do you have evidence that is actually happening? I know of two people who tried to learn it and just found it too hard, don’t think a better teacher or materials would have helped. The evidence is mixed but personal accounts certainly suggest that only a very small number of people could get to such a high level and improved teaching probably wouldn’t help much. When we are talking about such extreme skills, people have their plateau or maximum ability level which is mostly fixed.
The human population growing just pushes us along the asymptote faster, rather than changing it.
To me the data shows that there has been no reliable increase in intelligence in the last ~30 years https://news.northwestern.edu/stories/2023/03/americans-iq-scores-are-lower-in-some-areas-higher-in-one/ Once again it needs to be at the very top level to matter.
Any specialization advantage is already tapped out with string theory and similar. My worldview definitely does not apply to advances in a field like biology as there is lots of experimental data, the tools are improving etc. I would expect advances there without any obvious plateau yet.