Comment by srean

Yes but it was a fundamental mathematical achievement to see this equivalence. That knowledge had to emerge, be discovered. This eventually led to the theory of Galois fields.

The connection with rotation emerged naturally from a line of thought that initially had nothing to do with rotations. It was a consequence of a desire to satisfy distributive laws and maintain vector addition.

Connection between seemingly unrelated mathematical fields happen from time to time and those are considered events of surprise, understanding and celebration.