LLMs cannot be universal problem solvers through prompting alone because language itself is a bottleneck; some task families will always be unsolvable via prompts, no matter how much data or compute you throw at them.
This paper proves fundamental limits on what LLMs can learn through prompting alone. Using game theory and information theory, the authors show that language is a capacity-limited channel—when task complexity exceeds what can fit in a prompt, different tasks become indistinguishable to the model, creating an irreducible error floor that no amount of data or scaling can fix.