Algebra
Branch · 9th century onward, Baghdad and then Europe · Mathematics, stage 2: Map the branches
Algebra began as a set of general procedures for solving equations, written out in words by al-Khwarizmi in Baghdad and carried into Europe in Latin translation, where symbols gradually replaced the prose. Its second life started in the nineteenth century, when Galois attached a group of permutations to each equation and explained solvability in terms of that group's structure. From then on the subject studied the operations themselves, and Noether recast whole fields of mathematics in terms of structures defined only by the laws their operations obey.
What it claims
- Unknown quantities can be represented by symbols and manipulated by fixed rules.
- General procedures, not case-by-case tricks, settle whole families of equations at once.
- The rules of an operation can be studied as objects in their own right, which is what groups, rings, and fields are.
Key ideas
People
Sources
- Algebra Wikipedia
- History of algebra Wikipedia
- Arabic mathematics MacTutor History of MathematicsOn the period when algebra was created and on how much of it later reached Europe.
