Mulligan's "great searching eyes" are the first of many eyes that one becomes aware of in reading this book. Our chief physical access to most of the characters in Ulysses is through descriptions either of their clothes or of their eyes, and the eyes have it in terms of conveying information about their minds.
In Telemachus, Mulligan has "great searching eyes," "mobile eyes." Stephen's decision to disclose his grievance against Mulligan stirs "silver points of anxiety in his eyes." When he is clowning, his eyes blink "pleasantly"; they lose all evidence of "shrewd sense," "blinking with mad gaiety." But Stephen sees the shrewd sense, and he discerns Mulligan's intention to claim the key: "He will ask for it. That was in his eyes." He sees things in Haines' eyes as well: their "wondering unsteady" quality when he begins declaiming Irish to the old milkwoman; the "firm and prudent" quality they display as the Englishman looks out on the sea, his nation's dominion; the fact that, despite Stephen's wish to dislike the stranger, "the cold gaze which had measured him was not all unkind." (In Nestor, Stephen recalls that Haines' eyes were "unhating.")
Some textual controversy attends the first of these glimpses of a character's eyes. Gabler’s edition replaces “great searching eyes” with “grey searching eyes.” It is hard to prefer this change on aesthetic grounds. Losing the suggestion of intellectual spaciousness, Gabler's version gains in return only a possible symbolic suggestion that (as Gifford notes) Buck Mulligan may be similar to Athena, because she is called the “grey-eyed goddess” throughout the Odyssey. Such a correspondence appears shaky on several different grounds. The word sometimes translated as “grey-eyed” in English versions of the Odyssey, glaukopis, more properly means “with gleaming eyes.” Mulligan's eyes are described later in Telemachus as "smokeblue"—greyish, perhaps, but hardly grey. And even if both his and Athena's eyes are imagined to be grey, it is hard to think of Mulligan as both Stephen’s beneficent protector and his Antinous-like antagonist.