Large Language Models (LLMs) have brought about a profound revolution across various sectors, spanning from industry and economy to education and entertainment. While the advancement of LLMs has primarily relied on hardware such as GPUs and engineering technologies, the field is now entering a new phase that necessitates deeper engagement with scientific disciplines. The integration of mathematical and quantitative insights is crucial for driving the next wave of breakthroughs in the realm of LLMs. We will reevaluate the core tasks involved in the lifecycle of LLMs through an optimization lens, with a focus on enhancing the scientific understanding of key phases including pre-training, post-training, and serving. We will discuss specific tasks such as (distributed) low-bit training, pruning, quantization, prefill-decode disaggregation architecture, and the management of training chips in distributed/centralized settings. Our primary objective is to reduce the computation and memory footprint of LLMs throughout their lifecycle. We will also initiate two new concepts: Optimization Agents and Intelligence-Collaborative Computation.