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Does the Jones polynomial detect the unknot?
Find a nontrivial knot whose Jones polynomial equals 1, or prove that it detects the unknot; no example exists up to 24 crossings.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "geometry-topology" | |
| 5 | + ], | |
| 6 | + "type": "construction", | |
| 7 | + "also": [ | |
| 8 | + "proof" | |
| 9 | + ], | |
| 10 | + "source": { | |
| 11 | + "key": "frontiermath-open", | |
| 12 | + "name": "FrontierMath: Open Problems", | |
| 13 | + "url": "https://epoch.ai/frontiermath/open-problems/jones-unknot", | |
| 14 | + "id": "jones-unknot", | |
| 15 | + "curator": "Epoch AI", | |
| 16 | + "status": "unsolved", | |
| 17 | + "as_of": "2026-10-20", | |
| 18 | + "catalog": "0521c19bbd38" | |
| 19 | + } | |
| 20 | +} | |