Unravel
An interactive browser playground where students drag strands to form braids and watch the Burau matrix, Jones polynomial, and other invariants update in real time, with an AI tutor that explains what each invariant is telling them.
Math graduate students taking geometric topology or knot theory courses
- Drag-to-weave braid editor that outputs algebraic notation automatically
- Live Burau and Jones-polynomial panels that animate as the braid changes
- AI walk-through that explains each invariant in plain language using the student's own braid
- Companion module covering Markov moves and the open questions referenced in research papers
The Burau-faithfulness result for n=4 has just landed, and a new wave of topology students are being pointed to these classic open problems; they need something tactile to actually feel what 'faithful representation' means instead of staring at matrices.
Audience is tiny (math grad students in geometric topology) and adjacent braid-visualization GitHub repos show 0 stars/forks, suggesting limited grassroots appetite for such tools.GitHub - lufreitas0000/Braid-Group-Visualizations ↗The Burau representation of the braid group is faithful for n = 4 ↗
Existing tools cover pieces (KnotPlot for viz, Tim O'Leary/Liverpool for Jones polynomial) but none integrate drag-strands + live Burau/Jones updates + AI tutor — that combination is open.The KnotPlot Site ↗Jones Polynomial calculator ↗
Math grad students are a tiny pool with notoriously low willingness to pay — KnotPlot and Sage/Mathematica are free/institutional; AI tutor WTP studies show mixed/premium-skewed results.To Pay or Not to Pay? Investigating Students' Willingness to Pay for ChatGPT ↗
Burau-faithfulness-for-n=4 is a 70-year landmark that will draw sustained topology curiosity, and math education tools have very long shelf life (textbook-grade).The Burau representation of the braid group is faithful for n = 4 ↗
Algorithms for Burau matrix and Jones polynomial are well-documented; drag-strands UI is doable in WebGL/Canvas but producing math-accurate, aesthetically credible visuals for picky mathematicians is non-trivial.Braid Group Visualization ↗