|Era||Islamic Golden Age|
|Main interests||Mathematics, Medicine|
Al-Samawʾal ibn Yaḥyā al-Maghribī (Arabic: السموأل بن يحيى المغربي, Hebrew: שלמה בן יחיא אלמוגרבי; c. 1130 – c. 1180), commonly known as Samau'al al-Maghribi, was a mathematician, astronomer and physician. 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. His father was a Rabbi from Morocco.
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.
|Arabic Wikisource has original text related to this article:|
He also wrote a famous polemic book in Arabic debating Judaism known as Ifḥām al-Yahūd (Confutation of the Jews) or in Spanish Epistola Samuelis Maroccani and later known in English as The blessed Jew of Morocco.
"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..."