How to choose a maths related epq topic

I wished I could do a maths eqp but I finalised on doing a chemistry/engineering eqp as its more relevant to me. But during the time I wanted to pursue a math eqp I was going to do on.........

1) abstract and recreational maths eg: fractals, colatz conjecture, weird summations etc
2) ideas that changed and shaped maths eg: eulers identity, calculus
3) was maths invented or discovered?
4) Millenium problems and current solutions ( as gonna pick this)
5) space problem eg something like you're on a spaceship with limited fuel far away from earth how would you get to earth. And you would use differential equations, circular motion newtons law of gravitation and calculus to find an effective path back to earth.(this one is the best one in my opinion but it does take a bit of time to set up all the parameters and boundary condition tbf depends if you got the time and if your good at physics as well I am assuming to take FM, physics and something else if you want to do an eqp on maths)
Hope that helps.

Thank you very much, that helps a lot indeed. My first idea was on comparison of cellular automata and modelling the universe/ computability of the universe (complexity and chaos related). But it seems to be a bit bold. I then wanted to link it with fractals. Do you have any ideas on how to develop this any further?

I did a maths essay on whether maths invented or discovered, so this might be my back up choice if the others don't go well.

I really like the space problem and I will have a good think about it.

Another idea that popped out to me was about statistics: applications of normal distribution/ normal distribution in life.

Np
I am sure that there was a link between cellular automata and fractal especially the structures they look similar-ish and that would be fun. But if I had to say the space problem is the one I would pick just for the sheer fun of it and you can make it as difficult as you want. You don't have to do any "traditional" research as you're just doing maths and I think when it comes to presenting the epq I think it would a good one to do.
But at the end of the day, it's your choice.