Here are some papers its students published this year: https://www.bxscience.edu/apps/pages/index.jsp?uREC_ID=3719&...

A similar institute is the North Carolina School of Math and Science, and their current newsletter is here: https://broadstreetscientific.ncssm.edu/

This type of content is not representative of the average high school's mathematics curriculum in 1957.

The first group are the various local public schools (i.e. PS 153), the only requirement to attend is that you live in the neighborhood and aren't in jail. This is what all other city school districts have and the default (the vast majority of kids go to these). The quality varies by neighborhood from very bad to fairly good.

The second group are a bunch of specialized schools that focus on various trades/skills/careers. Examples are the transit high school, the fashion high school, multiple arts high school, etc. I think you have to apply and I think each school sets their own requirements, but generally speaking, the bar isn't super high.

The third group are the "selective" high schools. Schools like stuyvesant, townsend harris, bronx science, brooklyn latin, brooklyn tech, etc. To gain entrance to these, you have to take a standardized test and score higher than a certain level (there is currently no other requirement but that is under debate). These schools are better than 90% of elite private high schools... and free. As you might imagine, the competition to gain entrance is fierce. Some are more difficult to get into than ivy league universities. The caliber of students is very high and the education is...intense.

This school has produced 8 Nobel laureates.