<p>The potential for large language models (LLMs) to attain technological singularity—the point at which artificial intelligence (AI) surpasses human intellect and autonomously improves itself—is a critical concern in AI research. This paper explores the possibility of current LLMs achieving singularity by mentioning some frequently discussed philosophical issues within AI ethics and providing a theoretical framework for recursively self-improvement LLM. In this paper, we discuss the singularity phenomena that have been predicted in the past by pioneers of computer science and philosophers; how an intelligence explosion could be realized through the elemental technologies in modern computer science; and to what extent the metaphysical phenomena speculated by philosophers have actually approached reality. We begin with a historical overview of AI and intelligence amplification, tracing the evolution of LLMs from their origins to state-of-the-art models. We then propose a theoretical framework to assess whether existing LLM technologies could satisfy the conditions for singularity, with a focus on recursive self-improvement (RSI) and autonomous code generation. We integrate key component technologies, such as reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO), into our analysis, illustrating how these could enable LLMs to independently enhance their reasoning and problem-solving capabilities. By mapping out a potential singularity model lifecycle and examining the dynamics of exponential growth models, we elucidate the conditions under which LLMs might self-replicate and rapidly escalate their intelligence. We conclude with a discussion of the ethical and safety implications of such developments, underscoring the need for responsible and controlled advancement in AI research to mitigate existential risks. Our work aims to contribute to the ongoing dialogue on the future of AI and the critical importance of proactive measures to ensure its beneficial development.</p>