Question

When did algebra first start in math?

Answer 1

Short answer: very early — algebraic methods go back at least to ancient Mesopotamia (around 2000–1600 BCE). The subject then developed in several stages over millennia into the symbolic and abstract algebra we know today.

Brief timeline and milestones
- Babylonian math (c. 2000–1600 BCE): clay tablets show systematic procedures for solving linear and quadratic problems and manipulating unknowns numerically. These are practical, algorithmic methods rather than symbolic algebra.
- Egyptian and Chinese work (roughly 2000 BCE–1st century CE): problem-solving recipes for proportions and linear problems (e.g., The Nine Chapters in China).
- Greek mathematics (classical era): much “algebra” done geometrically (Euclid). Diophantus (3rd century CE) introduced a more symbolic, syncopated algebra in his Arithmetica and is often called the “father of algebra” for moving toward algebraic notation.
- Indian mathematicians (5th–12th centuries): Brahmagupta, Bhaskara II and others gave general solutions for quadratics and worked with zero and negative numbers.
- Islamic Golden Age (8th–12th centuries): Al‑Khwarizmi (9th century) wrote Al‑Kitab al‑Mukhtasar fi Hisab al‑Jabr wal‑Muqabala — the word “algebra” comes from al‑jabr. He systematized methods for solving linear and quadratic equations.
- European symbolic algebra (16th–17th centuries): François Viète introduced systematic use of letters for unknowns and parameters; Descartes advanced symbolic notation and linked algebra to geometry (analytic geometry).
- Modern abstract algebra (19th century onward): development of groups, rings, fields (Galois, Cayley, Noether, etc.), turning algebra into the study of abstract structures rather than just solving equations.

So: roots are ancient (Mesopotamia), major formalization came with Al‑Khwarizmi in the 9th century, and symbolic/abstract algebra developed later in the Renaissance and 19th century.