Comment by robinhouston

From some conversations on Twitter, it seems plausible that the rank-48 decomposition of the 4×4 matrix multiplication tensor really is new; and that perhaps where things have gone awry is attempting to summarise this result in a more lay-friendly manner: the algorithm in that post apparently doesn't constitute or imply a rank-48 tensor decomposition.

On the other side, it's claimed here that an algorithm that uses only 46 multiplications has been known since 1970: https://mathstodon.xyz/@fredrikj/114508287537669113