Fair enough, one misconception I always hear from people learning about Godel's incompleteness theorem or the halting problem is that it means there exist algor

Fair enough, one misconception I always hear from people learning about Godel's incompleteness theorem or the halting problem is that it means there exist algorithms where we can never know if it halts or not. Like there's some limit to math that makes it impossible for us to know whether a particular algorithm just keeps running forever or will eventually stop. No such algorithm exists, no such example exists because for any particular algorithm it's always possible to determine whether it halts or not (at least in principle). It might not be practical, the proof might be incredibly difficult, but math does not have any kind of intrinsic limitation that prevents us from proving whether a specific algorithm halts.