I respect that. However, I judge myself and value myself on my creative and intellectual output. I want to do stuff that is not trivial, and admittedly, this is a preference. I could teach piano and I'm sure I could be quite successful at it, but I don't like the idea of pushing the barrel down the road. My parents said that given what I knew now, I might let my kids take piano lessons so that they might grow up to be good pianists. I am admittedly selfish and have a bit of a chip on my shoulder about not having opportunities as a child to advance and actually become competitively good at an area of my interest.
It usually does require talent, effort and opportunity to become world class and many who have reached this level appear to have stepped up on the shoulders of others (parents, mentors, coaches) who have already navigated the pathways and were thus able to give the next generation a head start. I can understand why, as a plurally gifted individual with a lot of potential (still), who would have been willing to put in effort if appropriately motivated, you mourn that you haven’t received such an opportunity. That is valid, and it’s possibly a regret that some of us, and likely many others, have also experienced, but won’t, by itself, help you progress forward. I suspect that a lot of advice here comes from the wisdom of hindsight, of ways that mature individuals have navigated different pathways to other successes which we now feel are equally, if not more, fulfilling, but are not regarded, at least not by the general public, as ‘world class’. I don’t think the teen version of me would have appreciated my current values as someone who would now prefer to be at a dinner table conversing with jacks and jills of all trades who have led productive lives, rather than with monomaniacs (not that all world class achievers are necessarily such).
For both maths and music, some of my experiences may be relevant to yours. One of my parents led a carefree childhood and excelled at many sports (including selection into a school aged national team as an amateur) but regretted their lack of opportunity to learn music and so started me at a very young age. I was obedient and diligent, so with an early formal start, appeared precociously ‘talented’. However, as Indigo alluded, the regimented discipline my music teachers tried to enforce completely drowned my personal enjoyment and interest in music, such that after investing some ten years in practice and preparation for AMEB exams, when my parents allowed me to discontinue formal lessons in favour of spending my time on school studies, I stopped playing altogether. In contrast, I loved maths but received parental encouragement only so far as to achieve high marks at school. I borrowed books with Olympiad problems and worked through them myself and, like you, made it to the level of national finalist solely on my own steam. From what I observed of the backgrounds of other finalists, I believe I might have gotten further if I had been given support and earlier opportunities, so I am no stranger to the thoughts and feelings you’ve expressed.
I resolved to offer opportunities but not impose any expectations on my kids. They’ve all preferred to take their own routes of self-discovery and declined tutors of any kind although they’ve been happy to receive material resources such as instruments and equipment to pursue their interests, so with aptitude, effort and offered opportunities, they are choosing paths with many scenic detours rather than speeding to destinations. A recent experience highlights the benefits of this - DS, a self taught musician, performed at an eisteddfod and gained second place. The pianist in first place, who was clearly classically trained and played a well known, technically difficult, piece to perfection, bounded up to DS afterwards and asked him where he got the ‘awesome arrangement’ of the popular piece he played, hoping to download the manuscript. When he understood that the piece was DS’s own arrangement, he expressed surprise. The other youngster’s performance skills could potentially become world class if he continues to apply himself, but he was quite apparently impressed with the skills of a ‘Jack of all trades’. Whilst you have mentioned the possibility of performing and teaching, I wonder if you have considered exploring composition, as it is an area of music which others tend to enter later and one where innate musicality, creativity and other mental abilities are of greater consequence than commencement age.
BTW, DS is aiming to study R & D engineering to try to develop and eventually put his STEM skills and creativity to good use, but also intends to use his YouTube channel as an outlet for his interest in music composition and has taken up decathlon training as it appeals to his approach of continually aiming for PBs rather than aiming to be world class in a single event. He generously helps his less academically able classmates and reliably undertakes menial household chores, even often his sisters’ shares. I will consider myself to have been a successful parent if he doesn’t ever need to struggle with feelings of regret which previous generations have had to resolve.