Knot theory news:

Mark Brittenham & Susan Hermiller: 'Unknotting number is not additive under connected sum': https://arxiv.org/abs/2506.24088

If you have a knot tied in a loop of string then the 'unknotting number' is the number of times you would need to pass the string through itself in order to untie it. It was an old conjecture that the unknotting number of two knots tied in the same piece of string was just the sum of the unknotting numbers of the two knots individually. But this result shows that it can be easier to undo two knots when they're both tied in the same loop than it would be if they were each tied in separate loops.

#Knoten Fertigkeit
aus dem Wurf (oder: aus der lockeren Hand) heraus

Nr. 1 ist unter Seglern bekannt als #Webeleinenstek oder #Fenderknoten #Klemmknoten

Nr. 2 sieht nach #Palstek aus

Moin, kleines
#Knoten #KnowHow
zum Morgenkaffee
gefälligst?

Einer meiner Favoritenknoten.

2 knots: trefoil and pentafoil composed of rhombicosidodecahedra that can represent points as well #math #topology #geometry #geometrictopology #knots #knottheory

For Elsa Star Trewyn: Roelofs star dodecahedral polyknot and Kepler Star dodecahedral polyannuloid #math #knots #knottheory #topology #geiometrictopology

3D Printed Kepler-Roelofs dodecahedral polyknot Inspired by Johannes Kepler and Rinus Roelofs #mathart #3dprinting #3dprintedmath #stem #steam #knots #knottheory #polyknots #geometry #topology #math #art

I finally learned how to crochet! Why did o one explain how trippy this is! I can just will things into existence with string and hook? In 3d? Contemplating how each movement adds to the pattern, how the loops and knots function- it's crazy. This is surprisingly mathy. I'm so obsessed.

fellow knitters: when i use the long-tail cast-on, my plied yarns untwist, badly. what's wrong with my technique? #knitting #advice #yarn #knottheory #maybe

Massive congratulations to our Director, Professor Geordie Williamson, who was awarded the Max Planck-Humboldt Research Award for his work in #artificalintelligence and #knottheory
Read more https://bit.ly/4dYFbP9
@maxplanckgesellschaft @HumboldtStiftung

I think Knot Theory says that neither of these is actually in a knot, but what about the overall joining of the two? Is that a knot? Or does this sort of situation have some other specific name?

Two unbroken loops woven together but not linked like a chain.

The closest similar thing I could think of is Borromean rings. This seems different to me though.

A little pure #CSS 3D demo I made on @codepen last year: torus knot out of neon tiles https://codepen.io/thebabydino/pen/poqmrNg

I saw this @beesandbombs .gif https://x.com/beesandbombs/status/1497594041164185608 and got the idea I could CSS something like it, but then I never got to posting it publicly...

I'm sure I will think of this video each time I will tie a knot on my shoes or during sailing from now on :) Thanks for the link @len

"There is an entire branch of math simply devoted to knots – and it has changed the world. We’ll rope you in."
https://invidious.fdn.fr/watch?v=8DBhTXM_Br4

I'm having a bit of fun seeing how many versions of unknots I can twist this rubber bracelet thing into before I go to bed.

Where could I find a table of knot-sums, or one of different factorings of composite #knots?

I'm interested in finding composite knots that can be formed in more than one way, which seems like it should be a thing. I can find lots of enumerations but no "addition tables".

Does anyone know #KnotTheory by any chance?

I tried my hand at the recognition problem and had some insight as to how to trivially solve it, as well as generate all knots. But being such an old and hard problem im skeptical if i might be missing something.

I like that a "not knot" is a thing in #KnotTheory. I also like that knot theory is even a thing.

I bet a lot of fun limericks could be written about not knots.

I wonder if knot theory was a thing before #StringTheory came along?

Brunnian link.

https://en.wikipedia.org/wiki/Brunnian_link

Which of these are unknots?
https://www.futilitycloset.com/2023/11/11/a-tangle/

Does there exist an online interactive knot diagram manipulative thingie?

If there's a mathematical way to describe all knots in knot theory... There has to be a way to describe all possible s*x positions...?

Yet another great #Veritasium video!

How The Most Useless Branch of #Math Could Save Your Life https://www.youtube.com/watch?v=8DBhTXM_Br4 #knottheory #topology #watching