We sent them to various sports but my youngest found football via watching the World Cup, my eldest found swimming as we went surfing and he wanted to be better.
Their choices. We just facilitate.
I don't think providing them stimulus and opportunity is you finding it for them. Giving your child access to interesting people across various fields ensures they can learn about various intellectual pursuits. Treating them as a person with real ideas to consider ensures that they'll have the confidence to engage in the real-world as a peer. Giving them freedom and "down time" to explore their own ideas actually give them the time to find their own path.
Think of it as a vector, you can let them pick the direction, but you can ensure that they go far in that direction. They don't have to be a world-class mathematician, even being a well-respected local teacher is exceptional.
I think no matter what you do it will have a deterministic effect on your kid. If you're more responsive than deterministic they'll observe you for cues of who/what you have the most respect or adoration for and maybe seek to emulate it (or if they're rebellious, spite it). There's a fine line and moderation is important as with everything of course.