Joyce tells the reader of Ulysses three times that Leopold Bloom had once planned, among his many other lapsed schemes in the realm of phenomena, to answer a newspaper's challenge to “square the circle” (U, 15.2401, 17.1072, 17.1696). Bloom is of course preoccupied with financial gain, and the prize, according to a document in his desk, would have been a million pounds. Yet unlike the more mundane puzzles with which Bloom amuses himself on June 16, 1904 – how to cross Dublin without passing a pub, for instance – the challenge of squaring the circle suggests a deep connection with the workings of Ulysses itself. The problem first enters the text in “Circe” when Virag, the apparition of Bloom's grandfather, claims that Bloom had once “intended to devote an entire year to the study of the religious problem and the summer months of 1886 to square the circle and win that million” (U, 15.2399-401). The specific nature of that “religious problem” remains only implicit in Ulysses, but Virag's rhetorical association of the ancient problem of quadrature with theology is reiterated by the symbolic context of its later appearances in “Ithaca.”