Al-Samawal
Arab mathematician who developed techniques for polynomial arithmetic and division.
Who or what
Al-Samawal ibn Yahya al-Maghribi (c. 1130–1180) was an Arab mathematician from Baghdad who wrote "Al-Bahir" (The Dazzling), a major work on algebra.
He systematized operations on polynomials, including addition, subtraction, multiplication, and division of polynomials in multiple variables.
Why it mattered
Al-Samawal extended al-Karaji's arithmetization of algebra by developing explicit algorithms for polynomial division.
He treated polynomials as formal expressions, an important step toward symbolic algebra.
Key works and moments
He performed polynomial long division, a technique later rediscovered in Renaissance Europe.
He correctly handled the division of polynomials with multiple variables and negative exponents.
Further detail
He organized polynomial arithmetic using tables and algorithms that anticipated modern polynomial algebra.
Al-Samawal's "Al-Bahir" presented the first known formulation of the binomial theorem for for arbitrary .
Legacy
His polynomial algorithms were foundational for the development of symbolic computation.
His work influenced both Islamic and later European algebra.
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