Maths is amazing. You cannot say you were not spellbound when first discovering fractals or the application of fibbonnaci in nature. Come on you applied math tools.
every problem can either be solved by a computer, or approximated by a computer.
Fermat's Last Theorem and Riemann Hypothesis please!

loljk
Even the applied mathematics has beautiful theorems. The every day integrals and differentiation you use, where do you think all that comes from? That's right, the fundamental theorem of calculus, one of the most profound discoveries of mathematics, you might think differentiation and integration are brothers but that's because you have been taught that in highschool without any secondary thought of questioning it, who ever said (informally) "integration is the opposite of differentiation"? In fact, there was NO connection b/w differential mathematics and integral mathematics before the discovery of the FTC which connected these 2 branches of mathematics. You might be able to apply it but appreciate the predecessors who proved that for you to use. Without the pureness of mathematics, there would be no applications. Pure mathematicians are provers, applied mathematicians are users. However a true mathematician should appreciate both sides of its nature, what's the point of proving it if you're not going to use it in the present or the future? What's the point of using it if you don't even know what it means?
But anyways, back to luken's question, what I meant by studying beyond 12 is not just studying whatever you like (ofcourse that's good if you can it'd make you much more confident when tackling problems) but you could read more about topic you are studying in year 12. For example if you are doing integrals, maybe read the integrals chapter in Stewarts, that way, you will feel much more confident when doing year 12 questions, you will think it's childplay. There are countless other examples.