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)
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Celtic cross
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Celtic statue
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Chinese knot
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Boat Knot
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Fish hook
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Vortex
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Vaughan Jones
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William Thurston
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Louis H. Kauffman
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#KnotTheory, #Mathematics, #MathHistory, #MathExplained, #PureMathematics, #Topology, #MathVideos, #KnotInvariants, #AlexandreVandermonde, #CarlGauss, #LinkingNumber, #ReidemeisterMoves, #AlexanderPolynomial, #JonesPolynomial, #HyperbolicGeometry, #WilliamThurston, #VirtualKnots, #LouisKauffman, #KhovanovHomology, #MikhailKhovanov, #MathPioneers, #MathDiscoveries, #MathConcepts, #MathScience, #MathEducation, #MathLearning, #AdvancedMath, #MathResearch, #MathCommunity, #MathEnthusiast, #MathematicalStudy, #EducationalVideos, #KnotTheoryHistory, #MathInnovation, #KnotMathematics, #ScienceOfKnots, #MathTechniques, #MathTheories, #MathematicalResearch, #MathAndScience, #MathFacts, #HistoricalMath, #MathDevelopment, #MathematicalConcepts, #LearnMath, #MathJourney, #MathWorld, #KnotsInMath, #ComplexMath, #MathematicalHistory

[@shaneri]

awesome video! Knots and braids and links are very interesting! Thanks Luca and Sophia!

[@KELLY-hn8mk]

Nice video! Can you make a video about manifolds 😊.

[@dibeos]

Thanks for the nice comment!!! Yes, I’ll add to our list right now. We will post it soon 😎🤙🏻

[@SobTim-eu3xu]

Great video!)
I love it❤

[@dibeos]

Thanks!! I thought you’d like it 😉

[@SobTim-eu3xu]

@@dibeos Its simply true)
And I like the video quality of video, I'm pleasantly surprised)

[@dibeos]

@@SobTim-eu3xu give us more ideas hahaha we love making these videos. Probably next week will publish one about Category Theory. What do you think?