The mathematical sophistication of Rashi and the early Tosafists

Abstract

The mathematical sophistication of Rashi and the early Tosafists is investigated by quoting and analyzing several examples of Rashi and the Tosafists commentaries on talmudic excerpts of mathematical interest. In these examples, one may encounter fundamental mistakes, as well as some correct advanced mathematical ideas combined with clever cases as presented by the Tosafists. It seems reasonable to tentatively conclude that Rashi and the early Tosafists had no advanced education in geometry, although they were perfectly proficient in arithmetic. The more sophisticated geometrical material found is either sourced externally or is a result of the method of study instigated by Ri. This style of learning, distinct in its attention to detail and careful case construction, allows for realizations of geometric relationships. From a historical perspective, it can be argued these advanced ideas can be traced to Rabbi Abraham bar Hiyya, a Spanish mathematician c. 1100. It is notable that Christian Europe suffered from a lack of advanced mathematical study during the time of Rashi and the earlier Tosafists, and so the advanced ideas that entered into the Tosafists commentaries most likely derive from Arabic mathematics through Spanish influence.