The connection between knot simplification and free groups is very fascinating even though it seems obvious when you think about it, thanks for sharing!
Very interesting problem and a truly genial solution! Congratulations! But what about constructions, where the picture falls after k nails are removed? Do you have any ideas or insights how it can be done?
Thanks! To answer your questions, I know how to solve the puzzle if we remove k nails. Initially, I wanted to present the solution in this video, but I thought that it would be too much - the video would have reached at least 40 minutes and too additional theory would have been needed. However, I am seriously thinking of posting a new video in which I explain the solution of this second generalization.
9:15 -9:50 is so funny to me, you don't really explain anything, burp out a bunch of notation and just expect people to know what you mean yet proclaim how simple it is. up until that point the video was great and I enjoyed it, though whoever named them brunnian and borromean links should rot, they sound way too similar for something that is probably commonly taught in a large lecture halls.
@@stefanandmaths883 I think that breaking mathematical subject matter into clear and simple and short terms is a great difficulty for mathematicians . They should work on that because It can be done . It just takes someone with that extra skillset , that "je ne sais quoi !" . Those that can master that should prove to be Great Teachers !
@@edwardmacnab354 I am on the same page with you. I will try to improve my explanatory skills and I am sure I will manage to do this by keeping making videos.
@DemonixTB Thanks for your feedback! I tried to explain “superficially” what a free group means so that people who had not studied it before would get an idea of what I was doing. If I had explained rigorously what a Free Group means, I would have needed to talk about a lot of Group Theory and the video would have had 3 hours :). Anyway, thanks again for your feedback and I will try to explain the solutions better in the future videos. PS. I’ve accidentally deleted my reply to your comment, but I rewrote it ooops :)
The connection between knot simplification and free groups is very fascinating even though it seems obvious when you think about it, thanks for sharing!
Smecher video, esti primul roman pe care il vad in SoME
Hehe mersi!
just a high school student, yet such impressive mathematical intuition!
Thank you!
You are so brilliant. Continue 👏👏👏👏
This student is brilliant and I wish him success in life.
Looking forward to seeing more from you!
Thank you very much!!!
I just want Grant to keep the SoMe going n going...and more and more creators join in. This was great bro.
Thanks!!
Wasn't expecting the commutator to show up! Very fun problem
Thank you! I am grateful for all this positive feedback
That was a fun time! Didn't see it coming, and really enjoyed it!
Thanks! These comments really motivate me to continue making videos.
Great video!
Brilliant ideas and exposition!
Me, looking at the bottom knot at 3:21: ah, yes. Trivial.
Haha, Marc Lackenby is the head tutor for maths at my college so it was a fun surprise seeing him here.
What’s your college?
@@stefanandmaths883 St Catherine's College (Oxford, there is a St Catharine's in Cambridge haha)
Very nice!
Thanks! I really appreciate!
Very interesting problem and a truly genial solution! Congratulations! But what about constructions, where the picture falls after k nails are removed? Do you have any ideas or insights how it can be done?
Thanks! To answer your questions, I know how to solve the puzzle if we remove k nails. Initially, I wanted to present the solution in this video, but I thought that it would be too much - the video would have reached at least 40 minutes and too additional theory would have been needed. However, I am seriously thinking of posting a new video in which I explain the solution of this second generalization.
I regret you did not make the return journey, showing what Brunnian links this polynomial solution yields.
i dont know why but i just can't think about knots my mind just doesn't work i just can't understand their shape
It needs some practice
To visualise them better, I bought some rope and really tried to make some real “Borromean rings”, for example. See if it helps you too :)
Maybe you could focus more on giving some intuition that showing hard to digest proofs. Thanks for the vid!
"Genelarization" -> Generalization
Oops, I didn't see that typo :). I hope that it didn't stop you from enjoying this puzzle, though
👏👏👏
👏🏻
wow😳
☺️
9:15 -9:50 is so funny to me, you don't really explain anything, burp out a bunch of notation and just expect people to know what you mean yet proclaim how simple it is. up until that point the video was great and I enjoyed it, though whoever named them brunnian and borromean links should rot, they sound way too similar for something that is probably commonly taught in a large lecture halls.
@@stefanandmaths883 I think that breaking mathematical subject matter into clear and simple and short terms is a great difficulty for mathematicians . They should work on that because It can be done . It just takes someone with that extra skillset , that "je ne sais quoi !" . Those that can master that should prove to be Great Teachers !
@@edwardmacnab354 I am on the same page with you. I will try to improve my explanatory skills and I am sure I will manage to do this by keeping making videos.
@DemonixTB Thanks for your feedback! I tried to explain “superficially” what a free group means so that people who had not studied it before would get an idea of what I was doing. If I had explained rigorously what a Free Group means, I would have needed to talk about a lot of Group Theory and the video would have had 3 hours :). Anyway, thanks again for your feedback and I will try to explain the solutions better in the future videos.
PS. I’ve accidentally deleted my reply to your comment, but I rewrote it ooops :)