Lost in space: uncovering fundamental limits of large language models in complex, spatial problem solving

As agents based on Large Language Models (LLMs) are rapidly becoming assistive tools in the real world, it is important to understand the limits of their ability to reason and navigate in complex physical spaces. While LLMs have demonstrated impressive performance on many reasoning tasks, their spatial reasoning remains underexplored. We evaluated agents powered by five state-of-the-art open-source models on two complex spatial problems that humans excel at: the Tower of Hanoi (ToH) puzzle and the Tetris game. In contrast to humans, who are able to learn these tasks with ease and are able to interact with the environment with very little training, we find that the LLMs are badly lost in space. In the ToH task, the agents started well at low complexity levels but failed to find general, complexity-independent solution strategies that humans discover with little practice, culminating in performance collapse as task complexity increases. In Tetris, the models rarely produced legal placements, even in drastically simplified variants of the game. In both tasks, evaluating their paths in space relative to optimal or acceptable ones reflects a fundamental lack of understanding of physical space and its laws. Both tasks are fully describable in text, giving LLMs the best conditions to succeed; however, the agents still failed to follow the rules of the problems, diverged toward impossible paths, struggled to maintain objects and problem states, and did not demonstrate any understanding of gravity, rigid bodies, and solid boundaries. Altogether, these results highlight key differences between human and LLM problem-solving approaches and suggest an uphill battle in scaling purely language-based architectures into general problem solvers.