Using e.g. a single zettabit-sized look-up table to give the 64-bit result of a multiplication of two 32-bit numbers suffers from a similar problem. But if we're talking about practical concerns there are already faster methods than random access in >100 exabytes of memory. And if we're talking theoretical concerns your answer still hasn't addressed the question of how to multiply numbers fast.

Exactly.

So what I wrote debunks your assumptions and proves your argument wrong.

This is how conversations normally go.