Early algebra (Diophantus' Arithmetica)

What it is

A treatise solving determinate and indeterminate equations with an abbreviated notation for the unknown, its powers and subtraction. The first step from verbal rhetoric to algebraic symbolism.

The Chinese Nine Chapters (c. 100 BCE) and the Indian Sulba Sutras contain independent practical algebra; Diophantus's date ranges between 150 and 350 CE.

What it led to

• Diophantine analysis and number theory (Fermat annotated his copy)
• Arab (al-Khwarizmi, al-Karaji) and Renaissance (Bombelli, Viète) algebra
• The separation of algebra from Greek geometry
• Symbolic notation as a technology of thought

Built on

• Euclidean axiomatic geometryc. 300 BCE
• Babylonian algebra
• Euclidean geometry
• Greek alphabetic numeration

Made possible

• Algebra and algorithm (al-Khwarizmi)c. 820
• Al-Khwarizmi algebrac. 820
• Al-Qalasadi's algebraic notationc. 1450
• Symbolic algebra with letters1591
• Symbolic algebra1591
• Fermat Last Theorem statement and infinite descentc. 1637
• Proof of Fermat Last Theorem1994 (anuncio 1993)
• Symbolic algebraic notation

Links

Sources✓ verified 2026-09-23

• https://mathshistory.st-andrews.ac.uk/Biographies/Diophantus/
• https://en.wikipedia.org/wiki/Diophantus