New Knot Theory Discovery Overturns Long-Held Mathematical Assumption
8 days ago
- #knot-theory
- #topology
- #mathematics
- Neckties at fancy events can represent complex mathematical knots.
- Mathematical knots are studied in knot theory, a branch of topology with practical applications like understanding DNA coiling and molecular stability.
- Mathematicians consider two knots the same if one can be manipulated into the other without cutting.
- Each knot has an unknotting number, the minimum moves needed to turn it into a simple loop.
- A long-standing conjecture suggested that the unknotting number of combined knots is the sum of their individual unknotting numbers.
- Recent research disproved this conjecture by finding a combined knot simpler than the sum of its parts.
- A study by Brittenham and Hermiller showed a combined knot required fewer moves to untangle than expected.
- This discovery challenges existing notions of knot complexity.