If your brother would always rather stay home and study than go out with his friends, it would be accurate and a little bit mean to call him a wonk, or a nerd.
The noun wonk is an informal way of referring to an overly studious person. Wonk is as derogatory as words like "dweeb" or "geek," and it implies someone who is boringly focused on work or school — like your physics major friend "the science wonk." Extreme fans of politics are sometimes called policy wonks. The word originated in the 1950s from American student slang, possibly from the word wonky, or "shaky and unreliable."