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Isaac Newton

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There's a Wikipedia article about it, though it's not a very good article.

My question:

Is it more correct to say that the problem has been shown forever insoluble?

Or is it more correct to say that it cannot be solved by any known mathematical method?

(I understand there are special cases which are soluble. I understand that it can be "solved" by successive approximations, which grow increasingly inaccurate as the number of iterations increases.)

I'm not a mathematician or astronomer. I'm writing a book, in which I want to use this as an analogy for other things. I want to get it right.

It's my understanding that quantum computers, if they ever exist, will not have infinite computing power. If so, as far as I know, the three body problem will remain insoluble. Correct?

Thanks in advance.

Isaac