Louis Bromfield defined an "egghead" as a "a person of spurious intellectual pretensions" who is "over-emotional and feminine in reactions to any problem." An egghead is "emotionally confused in thoughts...a self-conscious prig, so given to examining all sides of a question that he becomes thoroughly addled while remaining always in the same spot."
If you want to know more about the history of eggheads, you may want to check out Aaron Lecklider's Inventing the Egghead: The Battle Over Brainpower in American Culture.
Rebecca Onion reviews it at The Chicago Tribune. Here is a taste:
As Aaron Lecklider's surprising history "Inventing the Egghead"
shows, the figure of the unworldly and fragile genius showed up across
postwar popular culture, in comic pop songs, science fiction, television
and theater. Lecklider shows how the suddenly omnipresent and mockable
egghead was a creature of its time, born of postwar anxieties over
Communism, gender roles and race. He argues that the national sport of
making fun of eggheads had far-reaching consequences. To stereotype
people interested in ideas as elite, "soft," white, and male was to
restrain the definition of intelligence — to "limit those for whom
intelligence was culturally available."
To make his argument, Lecklider has to show that before the Cold War,
a broad range of Americans admired the qualities later associated with
eggheadery. In his influential 1963 work on the topic, historian Richard
Hofstadter argued that anti-eggheadism — or, to strip the term of its
slang, anti-intellectualism — had been pervasive in American life all
along. Lecklider, on the other hand, thinks that instead of being a
particularly virulent manifestation of an ongoing strain of American
thought, the invention of the hated egghead represented an abrupt
departure from previous popular attitudes toward intelligence.
Ranging across bits and pieces of popular culture from the first half of
the 20th century, Lecklider presents us with a series of cases meant to
prove that before the Cold War, everyday people both respected
intellectual activity and claimed it for their own. In this "organic intellectual tradition," women, working-class people
and minorities redefined "intelligence" as a quality that the
marginalized could use to gain power. Moreover, "brainpower" was
democratic — transmittable through the ad hoc and cheap educational
vector of popular culture.