Ribet studied at Brown University and Harvard University. He received his PhD in 1973 from Harvard, where his advisor was John Tate. After three years of teaching in Princeton and two years of research in Paris, Ribet joined the Berkeley faculty in 1978.
Ribet works in number theory and algebraic geometry. He is best known for his proof that Fermat's Last Theorem would follow logically from the modularity conjecture, then a well-known unproved conjecture about elliptic curves. When Andrew Wiles obtained cases of this conjecture in 1995, Wiles obtained Fermat's Last Theorem as a corollary because of Ribet's prior work.
Ribet is a member of the editorial boards of numerous book series and research journals. He was elected to the American Academy of Arts and Sciences in 1997 and the US National Academy of Sciences in 2000. He was awarded the Fermat Prize in 1989 and received an honorary PhD from Brown University in 1998. He received the Brouwer medal from the Royal Dutch Mathematical Society (KWG) in 2017.
Ribet was inducted as a Vigneron d'honneur by the Jurade de Saint Emilion in 1988. He received his department's Distinguished Teaching Award in 1985 and again in 2013.