About 15 years ago (I'm terrible with dates) I was working with my old friend Brent Ridenour on a software project in the Bay Area. During that time Brent lent me a book on knot theory that reinvented my view of mathematics. I found the whole concept of mathematical knots - the unknot, prime knots, knot polynomials, etc. fascinating. It forced me to revisit some basic skills that I had embarrassingly lost, and learn numerous new concepts. Brent was kind enough to spend time walking his slow friend through the concepts. The most important thing I took away from the experience was the realization that past a certain point, one that I never reached in school, math becomes really, really interesting.In mathematics, knot theory is the area of topology that studies mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together to prevent it from becoming undone. In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.

Tags: knot theory, mathematical knots
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Dan Starr: Do you remember the name of that knot theory book? I'm intrigued by your mention of prime knots, knot polynomials and transformations applied to knots.I was afraid someone would ask this :-) Its been too long. I don't remember the title, but I'll ask Brent next time we talk. A prime knot, as you might expect, is a knot that cannot be decomposed into two nontrivial knots. Nontrivial just means they aren't simple loops (the unknot.) You can add prime knots by clipping them and joining the ends. This creates a composite knot.
Dan Starr: I like stumbling on to instructive tutorials about math topics which are palatable to students or people with basic math knowledge. Webpages like these were nonexistent when I was young and I think could be really useful for teachers to foster more curiosity in students.We were just having a conversation about this in the office. If someone had shown me basic knot theory in say, junior high, I would have spent a lot more time on math at a young age. I took a look at some high school math books at a friend's house the other day and they seem very much as I remember them - unnecessarily boring. Topology fields that are easy to visualize seem like a great way of getting young minds excited about math while driving home the essential point that math is about more than pushing numbers around. We leave the explanation of its abstractness, power and beauty until far too late in the educational process.
Dan Starr: Somewhat related: I'm a big proponent of open sourcing US educational plans and material - it can only improve things.I agree. I think the availability of free, high quality educational material is a good metric for the sophistication of a society. Everyone benefits in manifold ways.
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