Can Humpty Dumpty be Put Back?
Here’s something that every one of us knows from childhood: - It is the easiest thing to multiply two numbers, no matter how large they are (It may take time, but the “how” part is child’s play. Literally.); - But there is no easy way to find the factors of a number, other than hit and trial, which can take forever. Such operations (easy in one direction, but impossibly difficult in the other) are called “Humpty Dumpty functions”, after the most famous egg in history. This belief in the Humpty Dumpty nature of the problem of factorization is at the heart of most encryption algorithms, including the ones used for your financial transactions on the Internet. No mathematician has found a way to factorize a number easily; so the belief is well placed indeed. Or is it? In his book, The Man who Mistook his Wife for a Hat, Oliver Sacks noticed something very surprising about a...