I find the idea that 3 year olds naturally love numbers as convincing as the idea that 3 year old girls naturally love glittery crowns
You're not serious? Surely you can accept that not all 3 year olds are the same?
Some 3 year olds do naturally love numbers. As a two year old, all of ds1's games revolved around counting and grouping objects. Even before he knew his numbers he would have a paper and felt tip, a pile of bricks and would sit and move bricks from one pile to another, drawing a circle on his piece of paper for each one he 'counted'.
Now at age 6 his first choice of lazy-Sunday afternoon activity is me writing him a list of algebra equations and then marking his answers.
I get that people will scoff at this and find it difficult to believe, but I can assure you that ds1 was never hot-housed by me. I've supported him, helped him to learn things he found interesting, but everything has been led by him. Wrt algebra, he found one of my old maths A Level text books in a drawer a few months ago, flipped to a page of advanced quadratic equations that caught his eye and begged me to teach him how to do them 
So I did (obviously not at A Level standard!) and now algebra is his favourite thing to sit and do.
He also loves swimming, football, nature outings, soft play and lots of 'normal' little boy things if that helps. But he's very, naturally, mathematically minded and it really winds me up that some people have such a sneering attitude of 'Oh but a child could never enjoy such things' - um, yes, some do.