Baghdad and the Islamic world · c. 1130-c. 1180
Al-Samawal
Al-Samawal was mathematician and physician. He developed polynomial arithmetic, rules for exponents, and methods for handling negative powers.
Biographical and historical reference works document Al-Samawal’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Al-Samawal was mathematician and physician associated with Baghdad and the Islamic world. He developed polynomial arithmetic, rules for exponents, and methods for handling negative powers.
His tabular arrangement of coefficients resembles later synthetic organization of polynomials. 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 developed polynomial arithmetic, rules for exponents, and methods for handling negative powers.
Method, teaching, or application
His tabular arrangement of coefficients resembles later synthetic organization of polynomials.
Why this matters
The larger lesson
Al-Samawal 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. 1130
Life and working period
Al-Samawal worked as mathematician and physician in Baghdad and the Islamic world.
- Legacy
Lasting mathematical connection
His tabular arrangement of coefficients resembles later synthetic organization of polynomials.
Key idea
An algorithm is a dependable sequence
Al-Samawal’s work illustrates how a clear sequence of operations turns a difficult task into repeatable calculation.
Following multiplication before addition gives 15 × 14 + 4 = 214.
Try it yourself
Follow the operation order
Calculate 15 × 14 + 4.
- Multiply first.
- Add the remaining value.
- Check by estimating the size of the result.
Show the answer
15 × 14 = 210, and 210 + 4 = 214.
Math at work
Scientists and astronomers use the same habits
Scientists and astronomers use arithmetic to plan, compare, test, or communicate decisions. Al-Samawal’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
His tabular arrangement of coefficients resembles later synthetic organization of polynomials.
Al-Samawal matters because of only one famous formula or anecdote.
The documented record is broader: He developed polynomial arithmetic, rules for exponents, and methods for handling negative powers.
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.