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Goldberg was born in Pittsburgh, and was educated at yeshivot Torah V'Daat and Chafetz Chaim, as well as at the University of Pittsburgh, where he studied English literature. He was ordained at the Jewish Theological Seminary in 1941.
After serving as a chaplain in the United States armed forces during World War II, Goldberg moved to Israel to study at the Hebrew University in Jerusalem, where he remained until his retirement. In 1952 Goldberg received a PhD in Talmud from Hebrew University, with a critical edition of Massechet Ohalot serving as his dissertation.
After graduation, Goldberg served at the Hebrew University as professor and professor emeritus of Talmud, as well as chair of the Talmud department. He also served as visiting professor at the Jewish Theological Seminary and University of Pennsylvania.
Goldberg published four books: Critical editions of Massechtot Oholot, Bava Kamma, Eruvin, Shabbat and Tosefta Bava Kamma. He also published many articles in scholarly journals.
Goldberg was married to Rivka Abramowitz.
- In 1955, Goldberg was awarded the Rav Kook Prize from the city of Tel Aviv for his dissertation.
- In 2000, he was awarded the Israel Prize in Talmudic studies.
- "Israel Prize Official Site (in Hebrew) – Recipient's C.V.". Archived from the original on 2012-03-22.
- "Israel Prize Official Site (in Hebrew)- Judges' Rationale for Grant to Recipient". Archived from the original on 2009-10-19.