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Explore the fascinating connections between mathematics and everyday life in this 28-minute lecture by Jim Carlson from the Clay Mathematics Institute. Delve into the world of braids, knots, and links as part of the "Advancing Women in Mathematics Across the Americas" series. Discover how mathematical concepts like formalism, general position, and invariants relate to periodic tables and lengths. Gain insights into the equality question and its implications in both mathematical and real-world contexts.