Al-Samawal al-Maghribi

Al-Samawʾal ibn Yaḥyā al-Maghribī (Arabic: السموأل بن يحيى المغربي, Hebrew: שמואל בן יחיא המערבי; c. 1130 – c. 1180), commonly known as Samau'al al-Maghribi, was a mathematician, astronomer and physician.[1] Born to a Jewish family, he concealed his conversion to Islam for many years in fear of offending his father, then openly embraced Islam in 1163 after he had a dream telling him to do so.[2] His father was a Rabbi from Morocco.[3]

Samauʼal Al-Maghribī
Bornc. 1130
Diedc. 1180
Academic background
Academic work
EraIslamic Golden Age
Main interestsMathematics, Medicine
Al-Samaw-al Polynomial. Illustration of a book from Ibn Yahyā al-Maghribī al-Samaw'al called al-Bahir fi'l-jabr, meaning "The brilliant in algebra", from the 12th century.


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

He also used the two basic concepts of mathematical induction, though without stating them explicitly. He used this to extend results for the binomial theorem up to n=12 and Pascal's triangle previously given by al-Karaji.[4]


He also wrote a famous polemic book in Arabic debating Judaism known as Ifḥām al-Yahūd (Confutation of the Jews). A Latin tract translated from Arabic and later translated into many Western languages, titled Epistola Samuelis Marrocani ad R. Isaacum contra errores Judaeorum, claims to be authored by a certain R. Samuel of Fez "about the year 1072" and is erroneously connected with him.[5][6][7]


  1. ^ A Jewish Encyclopedia
  2. ^ UIMATH: Islamic Mathematics (Algebra)
  3. ^ Medieval Cultures in Contact, By Richard Gyug, pg. 123
  4. ^ Katz (1992), p. 242:

    "Like the proofs of al-Karaji and ibn al-Haytham, al-Samaw'al'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. Since al-Samaw'al did not have any way of stating the general binomial theorem, however, he cannot be said to have proved it, by induction or otherwise. What he had done was provide a method acceptable to his readers for expanding binomials up to the twelfth power..."

  5. ^ Williams, A. Lukyn (1935). Adversus Judaeos: a Bird's-Eye View of Christian Apologiae until the Renaissance. Cambridge: Cambridge University Press. pp. 228–232. ISBN 978-1-139-10847-8. OCLC 889963332.
  6. ^ Perlmann, Moshe (1964). "Samau'al al-Maghribī Ifḥām Al-Yahūd: Silencing the Jews / إفحام اليهود: تأليف السموءل المغربي (القرن السادس الهجري)". Proceedings of the American Academy for Jewish Research. 32: 5. doi:10.2307/3622414. JSTOR 3622414.
  7. ^ Samau'al al-Maghribi: Ifham Al-Yahud: Silencing the Jews 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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