Persia and Baghdad · c. 953-c. 1029
Al-Karaji
Al-Karaji was mathematician and engineer. He treated powers of unknowns algebraically and developed rules for polynomial arithmetic and mathematical induction-like arguments.
Biographical and historical reference works document Al-Karaji’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Al-Karaji was mathematician and engineer associated with Persia and Baghdad. He treated powers of unknowns algebraically and developed rules for polynomial arithmetic and mathematical induction-like arguments.
His work helped separate algebra from a strictly geometric presentation. Together, these contributions connect arithmetic and algebra and functions to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
He treated powers of unknowns algebraically and developed rules for polynomial arithmetic and mathematical induction-like arguments.
Method, teaching, or application
His work helped separate algebra from a strictly geometric presentation.
Why this matters
The larger lesson
Al-Karaji shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that arithmetic and algebra and functions can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- c. 953
Life and working period
Al-Karaji worked as mathematician and engineer in Persia and Baghdad.
- Legacy
Lasting mathematical connection
His work helped separate algebra from a strictly geometric presentation.
Key idea
An algorithm is a dependable sequence
Al-Karaji’s work illustrates how a clear sequence of operations turns a difficult task into repeatable calculation.
Following multiplication before addition gives 10 × 6 + 18 = 78.
Try it yourself
Follow the operation order
Calculate 10 × 6 + 18.
- Multiply first.
- Add the remaining value.
- Check by estimating the size of the result.
Show the answer
10 × 6 = 60, and 60 + 18 = 78.
Math at work
Engineers and architects use the same habits
Engineers and architects use arithmetic to plan, compare, test, or communicate decisions. Al-Karaji’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
His work helped separate algebra from a strictly geometric presentation.
Al-Karaji matters because of only one famous formula or anecdote.
The documented record is broader: He treated powers of unknowns algebraically and developed rules for polynomial arithmetic and mathematical induction-like arguments.
Keep exploring
Connected learning paths
Practice these ideas
- AdditionPractice adding whole numbers, integers, and decimals.
- SubtractionPractice subtracting whole numbers, including results below zero.
- MultiplicationBuild multiplication fluency with basic facts and larger values.
- DivisionSolve division problems with whole-number and decimal answers.
- Pre-AlgebraBridge arithmetic and algebra with integers, ratios, and equations.