I read that halting problem (https://en.wikipedia.org/wiki/Halting_problem) is undecidable. Does this means that it is not possible to prove it mathematically.
2026-03-28 07:48:25.1774684105
About undecidability and provability
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No. It means that we can prove (mathematically) that there is no Turing machine (which is a specific mathematical structure) that can decide whether a Turing machine halts on some given input. It's a mathematical non-existence theorem, just like we can prove that is no continuous retraction from $\Bbb R^n$ onto $\mathbb{S}^{n-1}$, and many others.