New Knot Theory Discovery Overturns Long-Held Mathematical Assumption

Abstraction: Wendt's 1937 additivity conjecture for knot unknotting numbers disproven after 88 years

Key points:

• Hilmar Wendt's 1937 conjecture — that the unknotting number of a connected knot equals the sum of the component knots' unknotting numbers — was disproven by Mark Brittenham and Susan Hermiller (University of Nebraska-Lincoln); preprint at arXiv:2506.24088
• They connected a knot with unknotting number 3 to its mirror image; the resulting knot requires only 5 moves (possibly fewer) to unknot, not the expected 6
• Unknotting number = minimum number of strand-crossing switches needed to convert a knot to a simple loop; often deceptively hard to compute
• Two knots are mathematically identical if one can be deformed into the other without cutting; only crossing switches yield distinct knots
• Finding shows that "our notions of knot complexity could have problems" (Rutgers mathematician Kristen Hendricks)
• Knot theory has practical applications in understanding how proteins coil DNA and how molecular structures remain stable

Connections: Knot Theory · Topology · Mathematics

Source: https://www.scientificamerican.com/article/new-knot-theory-discovery-overturns-long-held-mathematical-assumption/