[ArcticCelt]

7-year olds seams a bit young but Jason Roberts from Techzing through Math Academy has lead a program that got 10-year olds to get through calculus.

https://mag.uchicago.edu/education-social-service/can-fifth-...

https://outlooknewspapers.com/math-academy-multiplies-succes...

He told through the years his progress in his podcast (among other interesting things, like being one of the first developers at Uber and other fascinating stuff) https://techzinglive.com/

[rsj_hn]

In eastern europe the normal college-track educational path was to get a general education up until about thirteen which would cover the basics (what today we would consider a GED) and then you attend a gymnasium that focuses on a specific subject, for example music, or engineering, or foreign languages, etc. A thesis or project can be required to graduate from the subject which is then used as an entrance examination for a (three year) university, at which point you have what in the U.S. would be a strong masters degree. In the math gymnasiums, you not only learn calculus but also basics of abstract algebra, differential equations, topology, etc. Not advanced stuff, but basic stuff. But stuff that in the U.S. system is reserved for college, here it is taught in gymnasium (what used to be "prep" high school in the U.S.)

When you are young, that is the best time for you to learn these subjects. The only limitation is your ability to focus. For those who are young and are able to focus, they can do amazing things whether it is learning to play instruments, learning math, learning foreign languages, or learning any kind of trade. And historically pre-teens spent a lot of time learning, except it was with the family or another one-on-one apprenticeship scenario, so that by the time they reached teenager status they were already able to do useful stuff to support themselves and even got married. In modern societies, we tend to stretch education out farther and farther and simultaneously assume the young aren't able to learn as well as adults, when the opposite is true. Moreover we think that in the past, there was just less knowledge to absorb, but it is really the modern world in which de-skilling and mass production has made it so that a large proportion of the population is doing boring, repetitive, unskilled work, whereas in the past whether you were a baker or bricklayer or an organ player or a farmer you were doing skilled work, and you generally managed to learn the basics of that work before you became a teenager.