Why is Multiplication Hard?

Quick. What is 879544 * 528045? Unless you used a calculator or was some sort of savant you it would take you a couple of minutes to figure out a solution. Of course a computer can calculate this very quickly.



But what a computer can't do easily is learn how to multiply. If we feed in triples of numbers, (879544,582045,464438811480),  (541535,711245,385164061075), (230589,481621,111056504796), ..., into any machine learning algorithm it's doubtful the algorithm could take a new pair (666750,313009) and produce its product 208698750750. For if it could, then we should be able to use a similar algorithm to figure out how to factor numbers, which we believe a computationally difficult talk.



When you look at what machine learning seems to do moderately well: spam detection, face recognition, language translation, voice-to-text and self-driving cars, these are things that humans with a reasonable amount of training, can do very well.



Is this some philosophical argument that our brain works like machine learning algorithms? Think of it more as an observation.