China · c. 1260-c. 1320
Zhu Shijie
Zhu Shijie was mathematician and teacher. He developed multivariable polynomial methods and presented a sophisticated coefficient triangle.
Biographical and historical reference works document Zhu Shijie’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Zhu Shijie was mathematician and teacher associated with China. He developed multivariable polynomial methods and presented a sophisticated coefficient triangle.
The Jade Mirror of the Four Unknowns used up to four unknowns tied to heaven, earth, person, and matter. Together, these contributions connect 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
He developed multivariable polynomial methods and presented a sophisticated coefficient triangle.
Method, teaching, or application
The Jade Mirror of the Four Unknowns used up to four unknowns tied to heaven, earth, person, and matter.
Why this matters
The larger lesson
Zhu Shijie shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that 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. 1260
Life and working period
Zhu Shijie worked as mathematician and teacher in China.
- Legacy
Lasting mathematical connection
The Jade Mirror of the Four Unknowns used up to four unknowns tied to heaven, earth, person, and matter.
Key idea
An equation balances two descriptions
Zhu Shijie’s work shows how symbols can represent an unknown quantity while preserving equality.
In 6x + 4 = 40, subtracting 4 and dividing by 6 gives x = 6.
Try it yourself
Solve the equation
Solve 6x + 4 = 40.
- Subtract 4 from both sides.
- Divide both sides by 6.
- Substitute the result to check.
Show the answer
x = 6.
Math at work
Scientists and astronomers use the same habits
Scientists and astronomers use algebra and functions to plan, compare, test, or communicate decisions. Zhu Shijie’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
The Jade Mirror of the Four Unknowns used up to four unknowns tied to heaven, earth, person, and matter.
Zhu Shijie matters because of only one famous formula or anecdote.
The documented record is broader: He developed multivariable polynomial methods and presented a sophisticated coefficient triangle.
Keep exploring
Connected learning paths
Practice these ideas
- Pre-AlgebraBridge arithmetic and algebra with integers, ratios, and equations.
- Algebra IPractice equations, variables, functions, ratios, and inequalities.
- Algebra IIWork with quadratics, polynomials, systems, and sequences.
- GeometryExplore shapes, angles, area, perimeter, volume, and classification.
- Advanced GeometryPractice coordinate geometry, transformations, vectors, and solids.