Greek learning, input from India
*Hindu Arabic number system "modern"
*"Modern" view of algebra
Preservation and transmission of Greek Classics
Baghdad c. 8th century
House of Wisdom: translation and research
First book with "algebra" in the title
"Book of Al-Jabr and Al-Muqabala"
Al-Jabr 'transpose terms'
Al-Muqabala 'subtract equals from both sides'
Algorithm derives from Al-Kh.
very influential, no symbolic manipulation
Solutions in book appear in two forms:
1. Recipe "solution in numbers"
2. Proof by geometry
Persian, poet, mathematician, etc.
Wrote treatises on many topics
Treatise on cubics c. 1100
pull together complete theory
said algebra is NOT about finding unkowns
said Algebra and Geometry are the same
Efforts to prove 5th postulate
Al-Haytham: proposed solution
O. Khayyam: fallacious
Achievements of Arabic Math:
-Hindu-Arabic number system
-Preservation and Transmission of Greek classics