Al-Karaji

Al-Karaji was a Persian mathematician and engineer active around the turn of the 11th century. His writings helped establish algebra as a discipline operating on powers of unknowns, independent of geometric interpretation.

Algebra: A branch of mathematics that studies equations, symbols, and operations on quantities. Al-Karaji helped make algebra a systematic study of equations and unknown quantities.
Al-Khwarizmi: A ninth-century mathematician whose treatise helped establish algebra as a distinct discipline. Al-Karaji extended the algebraic tradition associated with Al-Khwarizmi beyond geometrical methods.
Ināth al-miyāh al-khafīyah: Al-Karaji's treatise on the engineering and management of underground waters. This work shows his practical expertise beyond algebra and arithmetic.
Omar Khayyam: A Persian mathematician, astronomer, and poet who classified and solved cubic equations geometrically. His later algebra developed within a tradition shaped by Al-Karaji's work on algebraic expressions.
Polynomial: An expression formed from constants and variables using addition, subtraction, and multiplication by nonnegative integer powers. His work treated expressions in powers of an unknown as objects for calculation.
Abu Kamil: A ninth- and tenth-century Egyptian mathematician known for algebraic work involving irrational and polynomial quantities. His algebraic methods preceded and influenced the tradition in which Al-Karaji worked.
Qanat: An underground water channel that conveys groundwater from higher terrain to settlements or fields by gravity. Qanats are among the water systems discussed in Al-Karaji's engineering writing.
Sharaf al-Din al-Tusi: A twelfth-century Persian mathematician known for influential work on cubic equations. His algebra reflects later stages of the mathematical tradition to which Al-Karaji contributed.
Mathematical induction: A proof method establishing a statement for all natural numbers from a base case and an inductive step. Al-Karaji used a form of induction in arguments about powers and sums.
Arabic mathematics: Mathematical scholarship written in Arabic across several regions and centuries, drawing on and extending earlier traditions. Al-Karaji's surviving mathematical works belong to this broad scholarly tradition.

Linked from 3 pages