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The faithfulness of the Burau representation of braid groups at n=4 has been unresolved for nearly ninety years. Recent research finally proves it faithful, with deep implications for knot theory, topological quantum computing, and cryptography.

The faithfulness of the Burau representation of braid groups at n=4 has been unresolved for nearly 90 years. A recent proof finally settles this critical case, with implications for knot theory, topological quantum computing, and cryptography.