[Herbstluft]

The logic you are presenting really overestimates the (important) daily work of the vast majority of people in math and programming.

It also overestimates the actual work and results these prodigies will eventually arrive at.

Very skilled mathematicians solve hard real world problems with math from the 17th century. None of them rediscover Calculus and linear algebra from scratch, and they also don't need to excel relative to the field oft mathematics or engineering. Nor will they move the field of mathematics forwards. That even goes for many very skilled researchers.

Very skilled programmers solve hard programming challenges by effectively "gluing" code blocks together others have created. They don't need to advance the field of computer science for this.

The idea that math, engineering or programming only make sense if you have a shot at rivaling the likes of Peter Scholze and Terence Tao or even popular programmers like Carmack is ridiculous.

Also: many child prodigies (like those kids finishing Masters degrees <20 and winning competitions at 14) are people you never hear from ever again afterwards because they move on to perform the same (still important) "mundane" tasks as anyone who finishes their degree at mid 20 or even 30.