Mulligan says, "I'm hyperborean as much as you," using a word that Friedrich Nietzsche applied to the Übermensch, the superman who will free himself from Christian ethics and transcendental metaphysics. Later in Telemachus, Mulligan playfully declares, “I’m the Uebermensch."
"Hyperborean" means literally “beyond the north wind” (the Greeks personified winds from the north as Boreas). Various ancient Greek writers referred to the home of hyperborean peoples as a kind of paradise, a place of perpetual spring, sunshine, and youth. The legend became popular in the nineteenth century and might have reached Joyce through many different sources, but the most likely one is Nietzsche.
Thornton notes the philosopher's use of the term in The Antichrist (1888, publ. 1895): "Let us face ourselves. We are Hyperboreans; we know very well how far off we live. 'Neither by land nor by sea will you find the way to the Hyperboreans'—Pindar already knew this about us. Beyond the north, ice, and death—our life, our happiness. We have discovered happiness, we know the way, we have found our way out of the labyrinth of thousands of years." Gifford adds that the adjective is used in The Will to Power (1896) to characterize the Übermensch.
Nietzsche's anti-Christian philosophy is almost certainly the operative context for Mulligan's earlier statement, because he is commenting on Stephen’s refusal to surrender to his mother’s request for a show of Christian piety. The more interesting question is how Mulligan, Stephen, and Joyce understand the German philosopher's ideas. Mulligan seems to find in his writings an inspiration for irresponsible, selfish hedonism. Stephen's thoughts are not made clear. There is good reason to think that Joyce, at least by the time he wrote Ulysses, may have come to a much more penetrating understanding of these writings.