alt Hacker NewsBy googling "4x4 matrices multiplication 48" I ended up on this discussion on math.stackexchange https://math.stackexchange.com/questions/578342/number-of-el... , where in 2019 someone stated "It is possible to multiply two 4×4 matrix A,B with only 48 multiplications.", with a link to a PhD thesis. This might mean that the result was already known (I still have to check the outline of the algorithm).
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wbhart • yesterday at 9:44 PM
As already noted in a post by fdej further down, Waksman's algorithm from 1970, which works over the complex numbers, requires only 46 multiplications (and I guess, divisions by 2, which may or may not be relevant depending on your actual ring).
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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