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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.

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    $\begingroup$ anything that computers do is done because a human has written out how to solve the problem in a bunch of tiny steps. The computer merely steps through those steps. $\endgroup$
    – Zo the Relativist
    Commented Jan 25, 2019 at 21:51
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    $\begingroup$ Related: physics.stackexchange.com/q/1235/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Jan 25, 2019 at 22:00
  • $\begingroup$ There has been recent discovery of new classes of solutions: sciencemag.org/news/2013/03/… $\endgroup$
    – JEB
    Commented Jan 26, 2019 at 0:21

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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.

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