In our book Why Machines Will Never Rule the World we argue that artificial general intelligence is mathematically impossible. Human beings and the processes that exhibit intelligence form highly complex systems whose behavior cannot be fully captured by any models we can construct, with or without computers.\ \ Proponents of modern machine intelligence offer two main lines of defense. The first is theoretical, based on universal approximation theorems for neural networks and the Church‑Turing‑Deutsch principle. The second is empirical, pointing to ever‑rising scores on standardized benchmarks.\ \ We first expose serious flaws in the physicalist argument that relies on the Church‑Turing‑Deutsch principle: it assumes any computable process can be physically realized, ignoring the fundamental constraints imposed by open‑ended, thermodynamically complex, non‑ergodic environments on cognitive behavior.\ \ We then review recent evidence showing that prominent benchmarks are compromised by training‑data contamination, flawed test construction, and strategic optimization toward specific metrics, meaning high scores do not equate to genuine cognition.\ \ Our central claim remains unchanged: models capable of performing cognitive behavior in open, thermodynamically complex, non‑ergodic settings are not attainable now and will not become achievable in the foreseeable future.\ \ Review