newtonian gravity - Why can't we humans solve the three-body-problem? and why can computers solve it?

Why is it that we humans can't solve the three-body-problem? (calculate the positions of the 3 bodies in a dynamical system)

And why can computers do it?

My thoughts:

Computers do it in way smaller steps then us humans, and if we tried to replicate what the computer does, it would take ages.

Answer

Computers can't.

You're right that they perform numerical integration way faster than we can, but, slower or faster, it's believed that neither people nor computers can solve the three-body problem. At least not in the sense of finding a closed-form, analytical solution.

These small-step calculations computers do produce only approximations to the solutions.

It's worth pointing out again, though, that the three-body problem is expected to be non-integrable. There's no proof yet.