The Doge

The best career advice for young people is to just focus relentlessly on 3 things: 1. Get skilled. Technical skills, writing skills, people-orchestration skills, everything. 2. Get involved contributing to a mission you're aligned with. It doesn't have to be pure bliss and your contribution doesn't have to match your top strengths exactly. But at the end of the day you have to feel some pride in what you did or what you learned. If you can find something like that while becoming skilled in a number of different ways then you'll find ways to increasingly wrap your skill profile around it (and you'll find/develop strengths in your skill profile that you never expected). 3. Pick up momentum. If you do (1) and (2) right then you've got direction and potential and all that's left is to sprint forwards and achieve it. The more momentum you pick up, the better you get, the more real value you produce, the more opportunities you create, the more you get noticed, the more value you capture into your own life, the more effort you want to put in... you create a virtuous cycle with so much momentum behind it that it becomes an unstoppable virtuous cyclone.

Mathematics is a highly interconnected network, not a hierarchical tree. What you're proposing is an incorrect and harmful understanding based on the outdated prevailing consensus. Learning should be a free exploration, not a prescription.