as-Samaw'al

As-Samaw'al ibn Yahya al-Maghribī ( Arabic السموأل بن يحيى المغربي, DMG as-Samawʾal b. Yaḥyā al-Maġribī ; born around 1130 near Baghdad ; around 1180 in Maragha / Iran ) was an Iraqi mathematician .

He was the son of the Jewish scholar Abu l-Abbas Yahya al-Maghribi, who came from Fez but then moved to Baghdad, and of Anna Isaac Levi from Basra . As-Samaw'al studied medicine and mathematics along with applications ( land surveying , astronomy ) in Baghdad . Since the level of mathematics teaching in Baghdad was not very high at that time, he continued his education, whereby he was particularly influenced by al-Karaji . He developed his algebraic methods in his first own treatise al-Bahir (The Radiance of Algebra), which also contains information about works by al-Karaji that are now lost (for example his introduction of Pascal's triangle ) and which he published at the age of 19. It advocates dealing with the unknown as with numbers. There he described the arithmetic of polynomials (also with negative exponents) and gave methods to find their zeros ( Horner's scheme ), and gave arithmetic operations for negative quantities (including rules of multiplication). In addition, following al-Karaji, he also dealt with Complete Induction . With this he proved the sum formula of successive squares:

${\displaystyle 1^{2}+2^{2}+3^{2}+\cdots +n^{2}={\frac {n(n+1)(n+2)}{6}}}$

He is also often credited with being the first to place (in modern spelling). ${\displaystyle x^{0}=1}$

He later traveled to Iraq , Syria , Afghanistan (Kohistan) and Azerbaijan , where he was staying in 1163 when he converted from Judaism to Islam. His justification for this decision is preserved. He did not inform his father of this until later, when he was in Aleppo - the father immediately went to see his son, but died on the way. He made a living as a doctor on his travels. He wrote other books, but few of them survive, such as elementary math textbooks and a book on sexuality, the only book he has received in the medical field. A book by him against astrology has also been preserved and a refutation of Christians and Jews.

Illustration from al-Bahir fi l-jabr

literature

• Adel Anouba: Al-Samaw'al, Ibn Yahya Al-Maghribi, Dictionary of Scientific Biography , Volume 12, pp. 91-95
• S Ahmad, Roshdi Rashed (editor) Al-Bahir en algèbre d'As-Samaw'al , Damascus 1972 (edition of his algebra)
• Roshdi Rashed, The development of Arabic mathematics: between arithmetic and algebra , London 1994
• Roshdi Rashed, L'induction mathématique: al-Karajī, as-Samaw'al , in: Archive for History of Exact Sciences, Volume 9, 1972, pp. 1–21
• Yvonne Dold-Samplonius , The solution of quadratic equations according to al-Samaw'al , in Boethius 12, 1985, pp. 95-104

Web links

• John J. O'Connor, Edmund F. Robertson :  As-Samaw'al. In: MacTutor History of Mathematics archive .