Generative Problem Solving: Bridging Classic and Modern AI

While Large Language Models (LLMs) have strong natural language understanding capabilities, they continue to face significant challenges in solving complex computational problems. In this position paper, we argue that a core limitation lies in the underdeveloped ability of LLMs to generate and explore diverse, meaningful problems while solving them with deeper reasoning. To address this gap, we introduce the concept of Generative Problem Solving (GPS) that emphasizes the capability of LLM for solving problems that require algorithmic reasoning.