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The matrix multiplication exponent, usually denoted by $\omega_{F}$, is the smallest real number for which any two $n\times n$ matrices over a field $F$ can be multiplied together using ${\displaystyle n^{\omega +o(1)}}$ field operations. My question is if $\omega_{F}$ is always a constant independent of the choice of $F$.

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    $\begingroup$ I believe that the current answer to this question is "we don't know". There's no obvious reason why $\omega_F$ would have to be field-independent, but for all we know at this point it could be the case that $\omega_F = 2$ for every field. $\endgroup$
    – Nathaniel Johnston
    Commented Jul 14, 2023 at 12:37

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