well, we can be fairly sure that Tom Bishop is NOT one.

Funny thing: he doesn't even realize that almost everything he says betrays him.

But there's something WORSE. He MAKES UP things. He FABRICATES things, out of thin air.

As in

few PhDs barely know what the Three Body Problem even is. When students do find and show an interest in it, they are often discouraged from looking into it as a thesis topic and are told that it is an impossible problem that will hurt their career to be associated with or to try to contribute to. They are also told the same when they show an interest in problems with Relativity.

(one wonders: how can he think he won't be proven wrong by someone who knows more than him? - which means a LOT of people)

Special Relativity is physicists' bread and butter.

And lots of people work in General Relativity (I, for one, graduated with a thesis in GR)

as for the Three Bodies Problem (which everyone knows about), maybe (actually, I don't know) it has been proven it has no analytical solution. As it has been proven that there's no general algebraic solution to an equation of 5th (or higher) degree. But give me a 5th degree equation and I will merrily and quickly solve it, by numerical methods, even on my pocket calculator.

In the same way, NOBODY is able to solve the quantum mechanical equations for the 26 electrons of the iron atom (and probably never will). So we use approximate methods to predict the spectroscopy of the iron atom and, as these predictions agree fairly well with observations, the theory IS confirmed. According to Tom, the iron atom should collapse, or fly apart. But the iron atom doesn't care a straw about what Tom thinks and merrily keeps its stability.

Yes, for SOME 3-bodies systems and for CERTAIN initial conditions (especially when the masses are comparable) you see, in simulations, that one body ends up being expelled. So what? For other initial conditions you see the system settling in a stable configuration. This is so much truer if, in a multi-body system, one body (the Sun) has a much bigger mass than others. The problem HAS been tackled, in the classical perturbation theory, and the conclusion is that the Solar System should be stable. And YES, maybe we don't have the ABSOLUTE certainty that perturbations from Jupiter and Saturn will not end up throwing Mars off its orbit in some billions of years. But if Tom wants to debunk the “helio model” it's up to HIM to prove that this MUST happen on a time scale of at most some hundreds millions of years. Good luck.

It's not a big mystery. The reason the problems are not taught is simply because they are lying to you. The purpose of science is to explain the world and to explain the universe, and if they can't do that then they will hide their failures.

the problems ARE taught. In many cases, at Ph. D. level. But if Tom had studied “Lectures on Physics” by Feynman (a text from the '60s, aimed at sophomores) he would have seen the author ending his exposition of the classical theory of electromagnetism with an excursus about open problems (and NO, this does NOT condemn the theory. It just simply shows its limits on an ultramicroscopic scale)

Just one thing more:

your model can't keep a planet and a moon in orbit around a star.

this is FE logic at its best. That is, worst.

a) SOME 3-bodies systems are unstable

b) Sun, Earth and Moon make a 3-bodies system

c) THEN, the Sun, Earth and Moon system MUST be unstable

Any more words needed?

(and now, if Tom Bishop comes up again with his Three Bodies Problem without first discussing this reply, EITHER he has not read it OR he's in total bad faith)