What Is Knot Theory? Why Is It in Mathematics? [pdf]
sci.osaka-cu.ac.jp
What Is Knot Theory? Why Is It in Mathematics? [pdf]
1–10 of 36 posts
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#2hey, I was just reading about Christopher Zeeman [1] who was quite the topologist. He founded the Maths Faculty at the University of Warwick [2].
Maths is a truly astonishing discipline begging the question, are we all just made of maths?
Zeeman was very quotable: "Technical skill is mastery of complexity while creativity is mastery of simplicity."
[1] Wikipedia entry - https://en.wikipedia.org/wiki/Christopher_Zeeman
[2] in memory of Zeeman - http://www2.warwick.ac.uk/knowledge/science/zeeman
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#3Topology has always seemed like the exotic yet substantive branch of mathematics... would love to see more reading like this posted.
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#4I think a lot of human understanding is basically intuition about topological invariants in various "spaces". If you go around asking famous thinkers what they see when they think they all describe similar kinds of imagery, fuzzy shapes that merge and unmerge in various ways as they probe the subject.
One good book I've found on the subject is https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From.
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#5I find it remarkable that it took humans so long (1849) to start mathematically investigating something as fundamental as knots.
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#6In the late 1800's knot theory was quite popular with physicists. Now there is the much bigger string theory:
https://www.sciencedaily.com/releases/2016/02/160210170411.h...
On a lighter note I could use some knot theory to explain why earphone or computer cables always seem to tie themselves up, despite my best efforts to keep them apart.
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#7I find it remarkable that it took humans so long (1849) to start mathematically investigating something as fundamental as knots.
Paper folding is something just as fundamental yet it wasn't until 1893 that humans started mathematically analyzing it.
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#8Reference: Kawauchi, Akio, and Tomoko Yanagimoto. "What Is Knot Theory? Why Is It In Mathematics?." In Teaching and Learning of Knot Theory in School Mathematics, pp. 1-15. Springer Japan, 2013.
http://link.springer.com/chapter/10.1007/978-4-431-54138-7_1
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#9In the late 1800's knot theory was quite popular with physicists. Now there is the much bigger string theory: https://www.sciencedaily.com/releases/2016/02/160210170411.h... On a lighter note I could use some knot theory to explain why earphone or computer cables always seem to tie themselves up, despite my best efforts to keep them apart.
Here's a paper on the topic:
"Spontaneous knotting of an agitated string" [1]
From the abstract: "We performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds. We used mathematical knot theory to analyze the knots."
Re: What Is Knot Theory? Why Is It in Mathematics? [pdf]
#10Knots can also be identified with spaces that don't seem "knotty" at first glance.
See Thurston's Knots to Narnia[1] and Not Knot[2]. PolyCut[3] is a little applet that can visualize these knotty portals.
[1] https://www.youtube.com/watch?v=IKSrBt2kFD4 [2] https://www.youtube.com/watch?v=zd_HGjH7QZo [3] http://facstaff.susqu.edu/brakke/polycut/polycut.htm