This talk draws from the paper “LLMs Will Always Hallucinate, and We Need to Live With This” and presents a critical analysis of hallucinations in large language models (LLMs), arguing that these phenomena are not occasional errors but inevitable byproducts of the models’ underlying mathematical and logical structures. Leveraging insights from computational theory, including Gödel’s First Incompleteness Theorem and undecidability results like the Halting, Emptiness, and Acceptance Problems, the talk will demonstrate that hallucinations arise at every stage of the LLM process—from training data compilation to fact retrieval and text generation. By introducing the concept of Structural Hallucination, we assert that hallucinations cannot be entirely eliminated through architectural improvements, dataset refinement, or fact-checking mechanisms. Instead, this work challenges the prevailing belief that LLM hallucinations can be fully mitigated, proposing instead that we must adapt to and manage their inevitability as a structural characteristic of these systems.