Andrew Rupinski asked a MathOverflow question about a knot invariant which he discovered, which distinguishes the left-hand trefoil from the right-hand trefoil. Nobody’s managed to identify this invariant yet, so maybe it really is new. The construction is by colouring vertices in a stick presentation of a knot by roots of unity, which is not something I’ve seen before, and is quite simple (you can read on MO exactly what it is- there are also pictures).
Finding a new knot invariant isn’t so exciting in as of itself, but a new perspective is a valuable thing to have, and, if nothing else, Rupinski’s question does seem to present a new perspective, at least to me. MathOverflow is becoming an ever more useful resource.