Knot Theory is Impossible Without These 9 Things

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Explore the historical roots and mathematical developments that transformed knots from simple practical tools into a crucial field of study in modern mathematics. Delve into the work of figures like Alexandre-Théophile Vandermonde and Carl Friedrich Gauss, and understand their contributions to the mathematical interpretation of knots.

Discover the intricate details of the linking number, Reidemeister moves, and knot invariants, including the Alexander and Jones polynomials, which have become fundamental in analyzing and categorizing knots. Learn how William Thurston's hyperbolic geometry revolutionized knot theory and how Louis H. Kauffman’s virtual knots expanded its horizons beyond three-dimensional space.

This video also highlights the significance of Khovanov homology, which bridges knot theory with algebraic geometry and category theory, offering deeper insights into the nature of knots. Perfect for math enthusiasts and anyone curious about the complex beauty of knots, this video provides a detailed yet accessible journey through one of mathematics' most intriguing fields.

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Image credits:

Matemateca (IME USP)

Celtic cross

Celtic statue

Chinese knot

Boat Knot

Fish hook

Vortex

Vaughan Jones

William Thurston

Louis H. Kauffman

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