I'd somewhat dislike real-world mathematics portrayed in the way you're looking for, because I, personally, care about maths accessibility and would like to uphold that many if not most people can learn to do even the most advanced subjects. There's an ongoing debate whether you need to be a genius to do mathematics. There are also two cultures in mathematics, of 'problem solvers' and 'theory builders'. Some areas of mathematics have easily stated problems that require little background, yet have very complex solutions that may perhaps require more of a stroke of 'genius'. Other areas are more scholarly in nature, and you need to immerse yourself in extensive literature and conceptual background. Also in the 21st century, mathematics like all science is increasingly becoming a collective effort rather than an individual one. An important part of mathematical progress is thus making it accessible to others. (None of this is to diminish the enormous impact that outstanding individual thinkers have had on various fields)
Now for the purpose of your fiction, it also needs to be credible why the society chooses to impose a significant risk on its children just to advance area X of mathematics, as important as it may be. I would instead begin from the purpose, and then find the required field of excellence to fit it.
The idea of enhancement for some purpose is a common and interesting one in fiction. 693
I'd say that technology is probably a better driver for such things than pure theory. So let me give some ideas (sorry if they don't answer the question directly).
* Particle physics. Say breakthroughs towards a Grand Unified Theory have been made, but the maths is ridiculously complicated. Nations/planets are in an arms race situation, and you need to have the next <PERSON> quickly.
* Quantum computation. With the widespread use of quantum computation, being able to visualize configurations of qubits in high-dimension space becomes an important advantage. We have the <PERSON> sphere for 1 qubit, but for n>1 visualizing all possible axes of correlation/entanglement becomes extremely hard.
* Navigation in 4d space. Think Dune's navigators. Generally any cognitive task arising from the neural connection of humans to machines
* Strategy. Think Ender's Game. 693