A significant leap in Large Language Model (LLM) capabilities has been observed in 2024-2025, moving beyond mere linguistic fluency to demonstrate a nascent form of algorithmic cognition. State-of-the-art LLMs have now achieved scores comparable to top-performing university students on challenging algorithms exams. This achievement is particularly noteworthy as these exams require robust reasoning skills to tackle complex, multi-step algorithmic challenges, indicating a deeper "understanding" of computational processes and logical deduction rather than simple pattern matching. While current LLMs still exhibit difficulties with certain graph-based tasks, their demonstrated proficiency in algorithmic problem-solving has profound implications for educational environments. The findings pave the way for LLMs to support instructors through the generation of high-quality editorial content, offering sophisticated and personalized feedback to students, thereby transforming the pedagogy of complex subjects by allowing AI to act as an intelligent assistant in cognitive domains previously exclusive to human experts.