Balbus, Mad Mathesis and Her Radiance deserve to be rescued from oblivion. The ten knots that form this intricate Lewis Carroll story show him as a teacher, mathematician and storyteller. Untangling the knots, solving the problems they hide, will require the ingenuity and imagination of the reader, which will allow him (or her) to escape for a while, like Alice, into the world of fantastic logic, where the rules are steadily observed.