Ibn Yaḥyā al-Maghribī al-Samawʾal السموأل بن يحيى المغربي، also known as Samau'al al-Maghribi (c. 1130 in Baghdad, Iraq – c. 1180 in Maragha, Iran) was a Muslim mathematician and astronomer of Jewish descent.[1] Though born to a Jewish family, he converted to Islam in 1163 after he had a dream telling him to do so [2] His father was a Jewish Rabbi from Morocco.[3] He was also a writer on Islamic medicine and Islamic theology.

Mathematics and astronomyEdit

Al-Samaw'al wrote the mathematical treatise al-Bahir fi'l-jabr, meaning "The brilliant in algebra", at the young age of nineteen.

He also developed the concept of proof by mathematical induction, which he used to extend the proof of the binomial theorem and Pascal's triangle previously given by al-Karaji. Al-Samaw'al's inductive argument was only a short step from the full inductive proof of the general binomial theorem.[4]

In Islamic astronomy, he wrote Exposure of the Errors of the Astronomers, which criticizes earlier astronomers in terms of both astronomy and mathematical trigonometry. According to the mathematics historians Taro Mimura, Glen Van Brummelen and Yousuf Kerai:[5]

By adopting a circle broken into 480 parts rather than the usual 360 degrees, al-Samaw’al found an ingenious solution to his complaint with his predecessors: he was able to compute an entire sine table using only purely geometric methods, without having to rely on the approximations that Ibn al-Haytham earlier had rejected.


In Islamic medicine, Al-Samawal wrote a medical treatise on sexual diseases and ailments.[5]

Polemic theologyEdit

He also wrote the famous polemic book debating Judaism known as Silencing the Jews (Refutation of the Jews) or in Spanish Epistola Samuelis Maroccani and later known in English as The blessed Jew of Morocco.[6][7]


  1. Jewish Encyclopedia
  2. Algebra, Islamic Mathematics, Department of Mathematics, University of Illinois at Urbana–Champaign
  3. Medieval Cultures in Contact, By Richard Gyug, pg. 123
  4. Katz (1998), p. 259:
    "Like the proofs of al-Karaji and ibn al-Haytham, al-Samaw'aldfbsebfiebfsdfuysefbuwfvusyefgvuywevfusevf's argument contains the two basic components of an inductive proof. He begins with a value for which the result is known, here n = 2, and then uses the result for a given integer to derive the result for the next. Although al-Samaw'al did not have any way of stating, and therefore proving, the general binomial theorem, to modern readers there is only a short step from al-Samaw'al's argument to a full inductive proof of the binomial theorem."
  5. 5.0 5.1 Taro Mimura, Glen Van Brummelen, Yousuf Kerai, Al-Samaw’al’s Curious Approach to Trigonometry
  6. Samau'al al-Maghribi Ifham Al-Yahud: Silencing the Jews / placeholder for Arabic language transliteration, by Moshe Perlmann
  7. Samau'al al-Maghribi: Ifham Al-Yahud: Silencing the Jews / placeholder for Arabic language transliteration by Moshe Perlmann, Proceedings of the American Academy for Jewish Research, Vol. 32, Samau'al Al-Maghribi Ifham Al-Yahud: Silencing the Jews (1964)


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