$$\log_4(49) = \log_2(7) \approx 2.8074 \qquad \log_4(48) \approx 2.7925$$

Equation 6 · Technological Evolution

Mathematicians Finished the Job After an Evolutionary Search Beat 56 Years of Human Proofs

This equation gives an approximation: it relates the quantities while allowing an approximation.

Because a genuine tensor decomposition composes with itself, the rank number converts directly into an asymptotic cost exponent, and DeepMind’s own paper does not spell out what that conversion yields — this is the article’s own arithmetic, shown rather than asserted. Applying Strassen’s 2×2 trick twice to reach 4×4 gives an algorithm whose cost scales as $n^{\log_2 7}$ ; applying it k times to reach a 2^k $\times$ 2^k matrix costs 7^k multiplications for n = 2^k , the same exponent however you slice the recursion. A genuine rank-48 4×4 decomposition, applied the same way, would scale as $n^{\log_4 48}$ instead: $\log_4(49) = \log_2(7) \approx 2.8074 \qquad \log_4(48) \approx 2.7925$. The gap is small — about 0.015 in the exponent, on the order of…

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