An impossibility theorem demonstrates that a particular problem or set of problems cannot be solved as described in the claim. Such theorems put limits on what is possible to do concerning artificial intelligence, especially the super-intelligent one. As such, these results serve as guidelines, reminders, and warnings to AI safety, AI policy, and governance researchers. These might enable solutions to some long-standing questions in the form of formalizing theories in the framework of constraint satisfaction without committing to one option. We strongly believe this to be the most prudent approach to long-term AI safety initiatives. In this paper, we have categorized impossibility theorems applicable to AI into five mechanism-based categories: deduction, indistinguishability, induction, tradeoffs, and intractability. We found that certain theorems are too specific or have implicit assumptions that limit application. Also, we added new results (theorems) such as the unfairness of explainability, the first explainability-related result in the induction category. The remaining results deal with misalignment between the clones and put a limit to the self-awareness of agents. We concluded that deductive impossibilities deny 100%-guarantees for security. In the end, we give some ideas that hold potential in explainability, controllability, value alignment, ethics, and group decision-making.