Beit Shammai (“house of Shammai”) was a school of thought originating with the sage Shammai, traditionally seen in rivalry with Beit Hillel. The school followed Shammai’s more exacting and literalist approach to Jewish law. Though influential enough to rival Beit Hillel in the late Second Temple period, that influence all but vanished with the Temple's destruction and the consolidation of Jewish law spearheaded by Hillel's intellectual heirs at Yavneh. According to the kabbalah, however, even though Jewish practice follows Beit Hillel in our times, it will follow Bet Shammai in the messianic period.
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