Impossibility Results in AI: A Survey

Perfect AI security is mathematically impossible: The paper's analysis of deductive impossibilities reveals that we cannot achieve 100% security guarantees in AI systems, meaning some vulnerabilities will inevitably remain regardless of how carefully systems are designed.

Explainability and fairness cannot always coexist: The authors present a new finding called "the unfairness of explainability," suggesting that making AI decisions more transparent and understandable may sometimes come at the cost of fairness—a critical tradeoff for regulators and developers to understand when implementing explainable AI requirements.

Fundamental limits exist on AI self-awareness and alignment: The paper identifies impossibility results related to self-awareness in AI agents and misalignment between AI systems (described as "clones"), indicating there are inherent constraints on how well we can make AI systems understand themselves or coordinate with each other.

Impossibility theorems should guide AI policy, not discourage it: Rather than viewing these mathematical limits as failures, the authors argue these results should serve as "guidelines, reminders, and warnings" for AI safety and governance—helping policymakers set realistic expectations and focus on achievable solutions.

Current impossibility theorems have significant limitations: The survey notes that many existing theorems are "too specific" or rely on "implicit assumptions," meaning their real-world applicability to AI governance may be narrower than assumed, requiring careful interpretation before applying them to policy decisions.