Many of the biggest math breakthroughs come from people early in their career.
[bg][bh]One of the things that makes children different and powerful is their imagination.
They don't have a prefrontal cortex that's fully formed, they are uninhibited, they can project themselves into a fantasy land more easily.
Our prefrontal cortexes aren't fully developed until around the age 26.
The prefrontal cortex is the part that curates your beliefs and says "that's dangerous" or "don't bother doing X, it won't work."
Before it's fully developed, you are able to play in spaces you don't yet know are supposed to be impossible.
Every so often, something in those spaces does turn out to be possible.
Children's lack of awareness of the impossible is a feature, not a bug.
That's what allows them to form self, adapt to a world their parents can't adapt to.