Mother Grogan is a mildly rude joke, characteristically brought up by Mulligan and quickly used to skewer Haines’ attitude toward Ireland and things Irish. Haines is collecting “exotic” Irish sayings and other folk esoterica, in the same way Bartok, Dvorak and Smetana collected ethnic folk tunes from the backwaters of the Austro-Hungarian Empire, as modernity began to overtake these regions. The implied condescension is obvious, especially to Stephen. It is alright for he and Mulligan to run down Irish culture; it is quite another thing for an Englishman, citizen of the reigning colonial power, to do so, and Mulligan quickly satirizes Haines’ study, asking Stephen if he thinks Mother Grogan is mentioned in the Mabinogion or the Upanishads. Since these are, respectively, the national epics of Wales, another Celtic nation incorporated into Great Britain, and India, Britain’s leading colony, Haines is being ragged quite pointedly.
On another level, Joyce is preparing the reader, sending up the epic tradition, and announcing his project of uniting high and low in “Ulysses”. He is using The Odyssey, part of what is in a sense the national epic of Europe, as the backbone of his project. His entire book is a questioning and sendup of the epic tradition by involving his protagonists in the most mundane incidents and actions, including rude jokes, the stuff of a Modern Epic. Mother Grogan may not be in the Mabinogion or the Upanishads, but she is in “Ulysses”.
– Andrew Levitas