Algebra and algorithm (al-Khwarizmi)

What it is

The Kitab al-jabr wa-l-muqabala systematised the solving of linear and quadratic equations as an independent discipline; his treatise on Indian numeral calculation gave rise to the word 'algorithm'. Algebra is born as a science.

'Algebra' comes from al-jabr (restoration); 'algorithm' from the Latinisation Algoritmi.

What it led to

• the Islamic mathematics of Omar Khayyam, al-Karaji and Sharaf al-Din al-Tusi
• the Latin translation at Toledo (Robert of Chester, 1145) and European mathematics
• formalised calculation procedures: the conceptual basis of computation

Built on

• Early algebra (Diophantus' Arithmetica)c. 250 CE
• Zero as a number (India)628
• Indian mathematics (Brahmagupta)
• Babylonian mathematics

Made possible

• Hindu-Arabic numerals in Europe976
• Trigonometry as a disciplinec. 980
• Zero and positional notation in Europe (Fibonacci)1202
• Liber Abaci and the Fibonacci sequence1202
• Symbolic algebra with letters1591
• Hindu-Arabic numerals in Europe
• symbolic algebra (Viète)
• Trigonometry as a discipline

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