The dialogue discussed below is found in The Roots of Political Philosophy, ed. Pangle (Ithaca: Cornell, 1987). A discussion of the dialogue’s authenticity is in the introduction of that work.
The Greater Hippias can be placed with the Protagoras and Gorgias as dialogues concerned with the value of sophistry and rhetoric. Protagoras begins with a myth and ends with Protagoras himself in the complications the concept of courage creates for holding mythos is reducible to logos. Gorgias argues to Socrates that without rhetoric, men could not possibly be free or exert rule; Callicles favors rhetoric because it is more manly than philosophy. The Gorgias ends with Socrates telling a myth.
The importance of the opening section of the Greater Hippias has implicitly been revealed. That section is about Hippias’ sophistic and rhetorical endeavors. He talks about how he had to learn things regarding the ancients in order to please the Spartans. Hippias is not only placed together with Protagoras and Gorgias formally in the Platonic corpus, but the question of how sophistry relates to the beautiful in earnest is raised. This is not an open and shut case of sophistry being entirely defective and philosophy carrying the day. Socrates needs Hippias as much as he needs himself, and we note that he willingly went to Protagoras and sought out Gorgias to ask about virtue and rhetoric, respectively. It may be the case that whatever claim sophistry has to the beautiful is more sound than any philosophy could make. Socrates’ physical appearance reveals him to be monstrous, erotic in such a way as to displease the poets.
A quick outline of the Greater Hippias: the opening has Hippias discuss his work in the service of Elea. He is an envoy to other cities, especially Sparta, where he discusses ancient things such as mythology to make money. His interest in things such as astronomy and geometry does not conflict with his political role(s) in the least; he speaks very well, and that power allows him to excel in both public and private endeavors. He claims wisdom has progressed, making this possible. Previous wise men in Greece were less focused on making money and getting power, but he seems to dwell on his ability to make money as proof of his excellence. From that opening, 281a-286c, the rest of the conversation becomes the quest for “the beautiful.” Hippias said he composed a very beautiful speech concerning what young men should strive for, and this piqued Socrates’ interest: What is the beautiful? Hippias then gives three definitions of what is beautiful: a maiden, gold, and a most honorable death. That, in turn, is followed by three definitions of Socrates: the beautiful may be “the fitting,” “the useful,” “the pleasant.” The dialogue gets markedly more difficult to understand as it progresses. That may or may not be related to a peculiar device Socrates uses throughout the discussion of “the beautiful.” Socrates says someone will abuse him if he cannot answer what is the beautiful and yet dare to proclaim something beautiful. That “someone” is responsible for holding Hippias’ and Socrates’ arguments to very strict standards. It turns out that “someone” is Socrates himself, but only we readers know this. Hippias cannot even recognize the name of his interlocutor when told it.
 Gorgias, 452d-e; 484d-e
 Greater Hippias, 281a-286c
 Socrates as monstrous: Leo Strauss, Xenophon’s Socrates (South Bend: St Augustine’s, 1998), 155. Also see: Seth Benardete, The Rhetoric of Morality and Philosophy (Chicago: University of Chicago Press, 1991), 104-5. For the displacement of the poets, see Seth Benardete, The Being of the Beautiful (Chicago: University of Chicago Press, 1984), xlii-xliii.