The Convergence of Judaism and Islam: Religious, Scientific, and Cultural Dimensions

10. Al-Khwarizmi’s Mathematical Doctrines in Ibn-Ezra’s Biblical Commentary

10 Al-Khwarizmi’s Mathematical Doctrines in Ibn-Ezra’s Biblical Commentary Michael Katz In the introduction to his Hebrew translation of Ibn al-Muthanna’s Commentary on the Astronomical Tables of al-Khwarizmi (780–845), Rabbi Abraham Ibn-Ezra (1089–1164) writes: ‫וחכמת‬ ‫החשבון‬ ‫חכמת‬ ‫סוד‬ ‫יודע‬ ‫בישמעאל‬ ‫גדול‬ ‫חכם‬ ‫קם‬ ... ‫וכל‬ .‫אלכואריזמי‬ ‫מוסי‬ ‫בן‬ ‫מחמד‬ ‫היה‬ ‫החכם‬ ‫וזה‬ ...‫העתים‬ ‫ומוציאים‬ ‫וחולקים‬ ‫כופלים‬ ‫האלה‬ ‫שבימים‬ ‫הערבים‬ ‫חכמי‬ ‫הלוחות‬ ‫מעשה‬ ‫כל‬ ‫הוציא‬ ‫והוא‬ ...‫החכם‬ ‫בספר‬ ‫ככתוב‬ ‫השורש‬ ‫באחרונה‬ ‫שוה‬ ‫שהיא‬ ‫התלמידים‬ ‫על‬ ‫קלה‬ ‫אחרת‬ ‫בדרך‬ .‫לדברים‬ ‫טעם‬ ‫נתן‬ ‫לא‬ ‫רק‬ ‫מהאינדיאה‬ ‫החכם‬ ‫כנכה‬ ‫למעשה‬ [There arose a great scholar in Ishmael who knew the secret of the wisdom of reckoning and the wisdom of times . . . and this scholar was Muhammad ibn-Musa al-Khwarizmi. And all Arab scholars nowadays multiply and divide and extract the root as is written in the scholar’s book . . . and he brought out all the tables’ work in another way, easy for the students, which is equal in the end to the work of Kanka the Hindu scholar, but he gave no reason for the words.] Ibn-Ezra is best known as one of the leading biblical commentators in the Judaic tradition. But in the wide spectrum of his writings we also find poetry , science, linguistics, philosophy, and mathematics. Specifically, mathematics is thoroughly and systematically studied in two books by IbnEzra —Sefer ha-Eh ad (Book of the Unit) and Sefer ha-Mispar (Book of the 172 r Michael Katz Number). The influence of the great ninth-century scholar Muhammad al-Khwarizmi is manifest in these books. Al-Khwarizmi’s impact is also noticeable in at least two other arithmetical manuscripts (in Hebrew and Latin) that have recently been attributed (not unreservedly) to Ibn-Ezra.1 Arguably, Ibn-Ezra was one of the first to convey to Europe the ideas of alKhwarizmi and with them certain fundamental doctrines of arithmetic.2 Muhammad ibn-Musa al-Khwarizmi was a scholar in Caliph alMamun ’s celebrated “House of Wisdom” in ninth-century Baghdad. He wrote extensively on mathematics and astronomy, and some of his writings were translated from Arabic into Latin, to be used as textbooks in schools throughout Europe from the twelfth century if not before. His best-known book is Kitab al-H isab al-Jabr w’al-Muqabala (Book of Calculus of Completion and Balancing). The term algebra was coined from alJabr and the term algorithm from al-Khwarizmi. Some scholars3 maintain that in writing this book al-Khwarizmi was influenced by (a translation of) a Hebrew manuscript entitled Mishnat ha-Midot (Study of Measures, by a mysterious Rabbi N). Other scholars4 disagree, and they are probably right. But that discussion is beyond the scope of the present essay. Another well-known book of al-Khwarizmi is Kitab al-H isab al-Hindi (Book of Hindu Calculus), bringing to the Arab world, and later to Europe , some basic ideas of Hindu mathematicians. Also worth noting here is al-Khwarizmi’s Istiqraj Tariq al-Yahud (Treatise on the Jewish Calendar ), where he discusses the nineteen-year cycle of the Hebrew calendar as well as the specific dates of Rosh ha-Shana (Jewish New Year) and several other Jewish festivals. What we want to show in this essay is that al-Khwarizmi’s fundamental principles were utilized by Ibn-Ezra not only in his mathematical writings but also, in a subtle yet substantial manner, in his biblical commentary. This is most clearly revealed in his extensive discussion of the Holy Name in chapter 3 of the book of Exodus. And this will be the focus of our attention in the present essay. The Holy Name The story of the first encounter between Moses and God is often devoutly rehearsed and seldom fully understood. Perhaps hardest to understand are the verses dealing with God’s name. We hear God speaking to Moses Al-Khwarizmi’s Mathematical Doctrines in Ibn-Ezra’s Biblical Commentary r 173 from the burning bush, ordering him to deliver the Israelites from slavery in Egypt. Moses at first maintains that he is unfit for the job, but God insists that he should do it. Then we read: ‫ואמרתי‬ ‫ישראל‬ ‫בני‬ ‫אל‬ ‫בא‬ ‫אנכי‬ ‫הנה‬ ‫האלהים‬ ‫אל‬‫משה‬ ‫ויאמר‬ ‫מה‬ ‫שמו‬ ‫מה‬ ‫לי‬ ‫ואמרו‬ ‫אליכם‬ ‫שלחני‬ ‫אבותיכם‬ ‫אלהי‬ ‫להם‬ ‫אהיה‬ ‫אשר‬ ‫אהיה‬ ‫משה‬ ‫אל‬ ‫אלהים‬ ‫ויאמר‬ :‫אליהם‬ ‫אומר‬ ‫אליכם‬ ‫שלחני‬ ‫אהיה‬ ‫ישראל‬ ‫לבני‬ ‫תאמר‬ ‫כה‬ ‫ויאמר‬ .(‫י”ד‬-‫י”ג‬ ,’‫ג‬ ‫)שמות‬ [And Moses said unto God, Behold, when I come unto the children of Isra-el and shall say unto them The God of your fathers hath sent me unto you; and they shall say to me, What is his name? what shall I say unto them? And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Isra-el, I AM hath sent me unto you. (Exodus 3:13–14)] These bracketed lines are taken exactly as they are, including capitals and punctuations, from the...