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Explore the longest mathematical proof in existence in this 20-minute video lecture on the proof of Schur number five. Delve into the concept of Schur numbers and learn how a 2-petabyte-sized proof was constructed. Follow along as the lecturer breaks down the problem-solving approach, reviews propositional logic, and explains the conversion process to propositional logic. Discover the role of SAT solvers in tackling this complex mathematical challenge and understand the importance of proof verification. Gain insights into advanced mathematical concepts and problem-solving techniques used in modern mathematics.