alt Hacker NewsMaybe I'm not communicating the point clearly. In order to use a table to do the whole multiplication it has to be much larger than the largest number you would want to multiply with it. A lot of the analysis of algorithms, especially multiplication as discussed here, is about astronomically large numbers, so you don't want the existence of an even more astronomically large table as a prerequisite.
We are talking about mathematicians. We are not talking about computer engineers trying to implement a physical GPU that can multiply matrices as fast as possible. You don't have to physically build the astronomically look up table by hand. One can simply state that it exists. Proofs do not have to be clean to be a proof. You might not "want" something in a proof, but if it works then it works.