The Knot Book
by Colin Conrad Adams · first published 2000
7mentions
5recommended by
7HN commenters
2015–2025first – last mentioned
71% recommend29% neutral
Why HN recommends it
Accessible, intuitive introduction to knot theory and topology that builds concepts like polynomial invariants step by step; suits readers with a pre-calculus background and those wanting a gentle entry.
Summarised by Claude from recommending comments
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…"curve" ? I am a big fan of this approach to learning mathematics, just forge ahead and when (if) things fall apart then go back and fix up the foundations. To this end I recommend a couple of books. "The Knot Book" by Adams is a very interesting exploration in topology (without requiring all the years of study at university before you are allowed to learn exactly what a topology is). And in another direction, group…
on “So you want to study mathematics” ↗For a gentile introduction, Colin Adams's "The Knot Book" is very accessible (and builds up the notion of polynomial invariants step by step).
on “A fast, strong, topologically meaningful and fun knot invariant” ↗…theory (TQFT). I don't know the physics, but I'm under the impression you can interpret it as having something to do with quantum states of anyonic particles. For books, you might look at Adams "The Knot Book" or Prasolov "Intuitive Topology" to get a substantial taste of knots and low-dimensional topology.
on “Graduate Student Solves Decades-Old Conway Knot Problem” ↗…can start with some. Feynman's Lectures on Computing. Scott Aaronson's Quantum Computing Since Democritus (though it assumes some background knowledge of quantum computing). I think Colin Adam's "The Knot Book" (on knot theory in topology) as well.
on “Ask HN: What kind of math do you study in your free time?” ↗…pre-calculus background. We used an early draft of a textbook (not sure of the title or if it’s even been released - our teacher got access because she knew the author) and a lovely knots textbook called “The Knot Book.” I think we gained a really good intuitive understanding of homeomorphism, neighborhoods, and homology groups. Knowing about these topics has been super useful in my studies and career. On the other…
on “Topology Illustrated (2015)” ↗I was inspired to make this after reading "The Knot Book" by Colin Adams. If you click "Rolfsen Table" at the bottom, you'll see the entire gallery.
on “Show HN: The prime knots in 3D” ↗The variant of this joke for mathematicians (source: https://jcdverha.home.xs4all.nl/scijokes/1_12.html): I saw the following in "The Knot Book" by Colin Adams (a very readable introduction to Knot Theory). The joke is attributed to Joel Haas. A woman walks into a bar accompanied by a dog and a cow. The bartender says, "Hey, no animals are…
on “CIA Declassified Coldwar Russian Jokes [pdf]” ↗