How can one make a child develop an interest in mathematics?
There is no way to make a child do anything, without causing harm, so just don't. How do you encourage a child? Well that's a different thing altogether.
But another question: why do you want to do that? Seriously, ask yourself how this desire can have any positive outcome at all.
I read the answer to another question on Quora today about whether using big words is a sign of intelligence. I'm not sure it is, but anyway, here is a big word: vicarious.
Experiencing something through another person's actions is called vicarious & it is a form of child abuse when applied by parents to children. What you are doing is projecting your own desires onto the child. The child will often comply because they are hardwired to try to please their parents. But later, they will resent you & may even learn to despise you. You have been warned. There are few emotions less pleasant than the feeling that your child thinks badly of you. It is well worth avoiding. If you try to live your life vicariously through your children, they will be miserable & later, maybe much later, you will be miserable too. All humans are unique. All children have things which engage them & things that do not. If you are lucky, there will be an intersection between the things that float your boat, and those which float your child's boat. But if not, & you decide that you are going to hammer that square peg into that round hole anyway, it will not end well.
My son turned out to be a pretty fine musician & writer. Now both of those skills are things I enjoy though I am considerably less talented in both fields than my afore-mentioned son. I caught a break there. But he also loved skateboarding, which is a total mystery to me & I had to give myself a very stiff talking to when I realised that I was in danger of favouring my prefered things (music/reading/writing) over his. I was right to be concerned & right to rapidly change course. My son is a person in his own right. I was partly responsible for his existence but that gives me no right whatever to expect him to do things just because they mean a lot to me.
The fact that when my partner & I saved up our pennies to buy him an American series Fender Stratocaster for Christmas one year, he was more thrilled than me, which was wonderful. But imagine the resentment I could have caused if his love for his scarlet strat was purely to please me. My pleasure the first time I heard him play Big Swifty by Frank Zappa & sang “City of tiny lights” from the same composer in a concert was unalloyed. That pleasure was accentuated by the fact that doing so was his choice, not mine.
Now my son is not much interested by mathematics which is a passion of mine & was my career up until my retirement. I helped him through his GCSE in maths but beyond that, he didn't care. And that's okay. I have no right to expect him to love maths in addition to loving the oeuvre of Frank Vincent Zappa. And rather than complaining at the former, I have always been delighted by the latter.
The secret here is to encourage your children to look for fun in as many different fields as you can. This will increase the probability that your child will ultimately find the thing(s) they love to do. The thing(s) that make them happy.
Now if my son had shown an interest in things mathematical, we'd have spent more time doing maths. As it was, we did a lot of music together. Though mostly I was a roadie by dint of being able to drive him & his band mates & their kit to gigs (and the fact that I, for all my love of music, am not a very good musician).
So don't decide ahead of time what you will encourage your child to love. Watch, listen to your child & think about what you see & hear. This will show you where your encouragement should fall.
I have high hopes for my 8 year old grandson on the maths angle based on the fact that he's pretty good at most things & is way cleverer than me. This became apparent when he was 3 years old & the two of us were playing with a model train set on a plain wooden circular track. He was pushing the train around in a counter clockwise direction and I told him that when something goes that way, it's called Anti-clockwise. Like an idiot & forgetting how young he was, I asked him “What do you think it's called when you go the other way?”. There was not even a pause before he blew me out of the water with “Uncle clockwise! And burst out laughing!”
All we do to keep him occupied these days is to present him with all kinds of stimuli & then sit back & see what happens. That's the adventure.