China · c. 1202-1261
Qin Jiushao
Qin Jiushao was mathematician and administrator. His Mathematical Treatise in Nine Sections developed congruence methods and algorithms for high-degree polynomial equations.
Biographical and historical reference works document Qin Jiushao’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Qin Jiushao was mathematician and administrator associated with China. His Mathematical Treatise in Nine Sections developed congruence methods and algorithms for high-degree polynomial equations.
The text applied mathematics to surveying, taxation, construction, and military supply. Together, these contributions connect arithmetic, algebra and functions, and geometry and measurement to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
His Mathematical Treatise in Nine Sections developed congruence methods and algorithms for high-degree polynomial equations.
Method, teaching, or application
The text applied mathematics to surveying, taxation, construction, and military supply.
Why this matters
The larger lesson
Qin Jiushao shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that arithmetic, algebra and functions, and geometry and measurement can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- c. 1202
Life and working period
Qin Jiushao worked as mathematician and administrator in China.
- Legacy
Lasting mathematical connection
The text applied mathematics to surveying, taxation, construction, and military supply.
Key idea
An algorithm is a dependable sequence
Qin Jiushao’s work illustrates how a clear sequence of operations turns a difficult task into repeatable calculation.
Following multiplication before addition gives 18 × 4 + 18 = 90.
Try it yourself
Follow the operation order
Calculate 18 × 4 + 18.
- Multiply first.
- Add the remaining value.
- Check by estimating the size of the result.
Show the answer
18 × 4 = 72, and 72 + 18 = 90.
Math at work
Carpenters and builders use the same habits
Carpenters and builders use arithmetic to plan, compare, test, or communicate decisions. Qin Jiushao’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
The text applied mathematics to surveying, taxation, construction, and military supply.
Qin Jiushao matters because of only one famous formula or anecdote.
The documented record is broader: His Mathematical Treatise in Nine Sections developed congruence methods and algorithms for high-degree polynomial equations.
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.