China · c. 1238-c. 1298
Yang Hui
Yang Hui was mathematician and teacher. His books preserved algorithms, magic squares, root extraction, and the triangular arrangement of binomial coefficients.
Biographical and historical reference works document Yang Hui’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Yang Hui was mathematician and teacher associated with China. His books preserved algorithms, magic squares, root extraction, and the triangular arrangement of binomial coefficients.
He included worked problems and criticism of common calculation errors, giving his texts a teaching focus. Together, these contributions connect arithmetic, algebra and functions, and statistics and probability to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
His books preserved algorithms, magic squares, root extraction, and the triangular arrangement of binomial coefficients.
Method, teaching, or application
He included worked problems and criticism of common calculation errors, giving his texts a teaching focus.
Why this matters
The larger lesson
Yang Hui shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that arithmetic, algebra and functions, and statistics and probability can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- c. 1238
Life and working period
Yang Hui worked as mathematician and teacher in China.
- Legacy
Lasting mathematical connection
He included worked problems and criticism of common calculation errors, giving his texts a teaching focus.
Key idea
An algorithm is a dependable sequence
Yang Hui’s work illustrates how a clear sequence of operations turns a difficult task into repeatable calculation.
Following multiplication before addition gives 13 × 12 + 5 = 161.
Try it yourself
Follow the operation order
Calculate 13 × 12 + 5.
- Multiply first.
- Add the remaining value.
- Check by estimating the size of the result.
Show the answer
13 × 12 = 156, and 156 + 5 = 161.
Math at work
Merchants and business owners use the same habits
Merchants and business owners use arithmetic to plan, compare, test, or communicate decisions. Yang Hui’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
He included worked problems and criticism of common calculation errors, giving his texts a teaching focus.
Yang Hui matters because of only one famous formula or anecdote.
The documented record is broader: His books preserved algorithms, magic squares, root extraction, and the triangular arrangement of binomial coefficients.
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.