December 18, 2025
Knot your average syllabus
Online Textbook for Braid groups and knots and tangles
A free math book on braids and knots sparks love, jokes, and a code-vs-chalk fight
TLDR: A free online textbook makes braids, knots, and tangles easy with puzzles, videos, and some code examples. Comments split between fans wanting the whole thing powered by a math software system and purists preferring readable lessons, with shoutouts for Mojo GPU puzzles and more animations.
Math class just went full pop culture: a free online textbook turns braids, knots, and tangles into a bingeable tour with puzzles, dances, and videos. It strolls from braids and permutations to "rational tangles" (yes, an actual dance), then into knot diagrams, color tricks, and famous invariants — with SageMath examples sprinkled in and a GNU free license so you can remix away.
In the comments, the vibe swings from wholesome nerd joy to spicy feature demands. N_Lens gushes, "I’ve always found braids & knots very fascinating," while jokers wonder if shoelace tying now counts as homework. The main drama: should the whole book run on a computer algebra system? falcor84 says do it — build it on code — and a chorus of programmers cheers for live, clickable maths. Meanwhile, chalk-and-string purists clap back: keep it readable, keep it human.
There’s a side quest too: folks shout out Mojo language GPU Puzzles and slick manim animations, begging for more visuals baked into the lessons. Others love the low-tech charm: hands-on tangle moves, the classic three-color puzzle, and clear, beginner-friendly explanations. Whether you want IDE-integrated math or bedtime braid lore, this resource has everyone tangled — in the best way.
Key Points
- •The textbook is organized into three sections: braids and permutations; rational tangles; knots and links.
- •Section 1 covers the relationship between braids and permutations, introduces “Anagram Algebra,” and discusses braid invariants and links to knot theory.
- •Section 2 explains rational tangles, connects them to continued fractions, and presents rational knots using Conway notation, with objectives and videos.
- •Section 3 addresses knot diagrams and invariants, includes a three-coloring problem, and examines coloration and the Alexander polynomial, with objectives and videos.
- •The resource section notes that the material is licensed under the GNU Free Documentation License.