Hmmm... I'd say that the problem is formulated in a way that allows for some maths, but in the process loses some of its essence.

For example, the 'proof' only talks about the length of the hypothesis, because that can be easily quantified. However, that does not rule out very short pseudo-explanations like 'god did it' or 'it's magic'. To rule out those, in practice one would need to introduce some non-mathematical language about what language is acceptable -- but that would make it very hard to reason about it mathematically.