4 ms·
The article seems to be implying that mathematicians study knots because there's lots of fun to be had. This is partly true, but there's other more profound rea
by mathgenius 4y ago
The article seems to be implying that mathematicians study knots because there's lots of fun to be had. This is partly true, but there's other more profound reasons. For example: higher dimensional algebra. The "usual" algebra is just one dimensional, but people have noticed that in many cases this is just a projection (shadow) of higher dimensional systems, where the symbols can interact in more than just a linear direction. And once you get to three dimensions hey presto your algebra can get knotted!
- macrolocal 4y agoAlso, knot complements are an important class of 3-manifolds.
- ouid 4y agojust a little further than that and every 3 manifold is surgery on a link.
- taliesinb 4y agoI would love to have some pointers to the higher dimensional algebra you're referring to.
- shagie 4y agohttps://youtu.be/EBWP1POPc2A https://youtu.be/EBWP1POPc2A and the associated knot theory from that university - https://www.youtube.com/c/MathatAndrews/search?query=knot https://www.youtube.com/c/MathatAndrews/search?query=knot
- mathgenius 4y agoJohn Baez has written a lot about this stuff. Try this: https://arxiv.org/abs/0903.0340 https://arxiv.org/abs/0903.0340 . There's also his TWF column.