Rabinovitch taught Judaism in several places and served as a congregational rabbi. Between 1952 – 1963, he was the rabbi of the Jewish community in Charleston, South Carolina. In 1963, he was called to serve as a community rabbi in Toronto. In the 1970s, he completed a Ph.D. in the field of statistics and probability in the Talmud at the University of Toronto; the results are in his book, Probability and Statistical Inference in ancient and medieval Jewish Literature. This topic was also explored by Australian Professor of Mathematics, Michael Hasofer. At that time he also gave lectures at the university and was an editor of the Rabbinical Council of America's journal "Hadarom". Rabinovitch also lived in London, where he served as dean of the London School of Jewish Studies and had a reputation as an influential scholar. Chief Rabbi Lord Jonathan Sacks became his protege. He later agreed to be a head of Yeshivat Birkat Moshe in Ma'ale Adumim, Judea and Samaria, a Hesder institution, and he was named rosh yeshiva there in 1982. In 2015 he led the Giyur K'halacha conversion court, of which he was one of the founders.
Philosophy
Rabinovitch was an authority on Maimonides; he published scientific, theological, and halachic books and essays on Maimonides' writings. His philosophical approach is influenced by Maimonides' rationalism. It emphasizes the connection between philosophy and halacha, between Torah and scientific studies, and between theoretical learning and practical application in life. In an interview, Rabinovitch said that he backed religious studies for women, and did not see a problem in Halachic decisions taken by women. However, he signed a letter agreeing with the Chief Rabbinate's opposition to religious women serving in the IDF. While many interpret Jewish law as speaking of monarchy as an ideal, Rabinovitch has supported a modern and liberal democracy with rule of law as the optimal form of government.
Rabinovitch was a religious Zionist and an opponent of the Oslo Accords. However, he was also more liberal in social and religious matters than many in the religious Zionist movement..
Selected works
Hebrew
Yad Peshuta Commentary on Maimonides' halachic book "Mishne Torah" - 14 volumes.
Melumdei Milchama - Responsa on halachic questions about military service
Darkah shel Torah - halakhic-philosophical actual essays
Hadar Itamar - Finis on the Talmud
Iyunim be-Mishnato shel ha-Rambam
Siach Nachum - Responsa on halachic questions
Mesilot Bilvavam - Halakhic-philosophical essays on Society and Statehood
English
Rabbi Hasdai Crescas on Numerical Infinities - Isis, Vol. 61, No. 2, pp. 224–230
Studies in the History of Probability and Statistics. XXII: Probability in the Talmud - Biometrika, Vol. 56, No. 2, pp. 437–441
Torah and Science: Conflict or Complement - Challenge: Torah Views on Science and its Problems, Feldheim Publishers pp. 44
Torah and the Spirit of Free Enquiry - Challenge: Torah Views on Science and its Problems, Feldheim Publishers pp. 54
The one and the many: Early stochastic reasoning in philosophy - Annals of Science, Volume 34, Issue 4 July 1977, pp. 331 – 344
Halachah and Technology - Proceedings of the Associations of Orthodox Jewish Scientists, Volume 2 pp. 129–149
All Jews Are Responsible for One Another - Jewish Tradition and the Nontraditional Jew. Ed. Jacob J. Schacter. Northvale, NJ.: Aronson, 1992 pp. 177–204