The last IMO problem AI could not solve

The 2025 International Math Olympiad’s sixth problem serves as a critical benchmark for the limits of artificial intelligence in creative, rigorous mathematical reasoning. While AI models have achieved rapid success in competitive math, they struggle with the patience and aesthetic appreciation required to solve problems that demand deep, non-rote insight. The tiling puzzle—which requires placing rectangular tiles on a grid to satisfy specific row and column constraints—demonstrates that optimal solutions often emerge from recognizing symmetric patterns, such as those linked to square numbers. Beyond the numerical result, the process of solving this problem highlights the necessity of "motivated explanations." These narratives provide the intuition behind a proof, distinguishing human mathematical practice from mere computational output. Elevating these explanations to the same status as formal proofs is essential for measuring true academic progress as AI continues to reshape the mathematical landscape.