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Jade Mirror of the Four Unknowns was written by Zhu Shijie, the greatest Chinese mathematicians lived during the Yuan Dynasty, in 1303. With this book, Zhu brought Chinese algebra to its highest level. It contains 288 problems for solution, of which four illustrate his method of the four unknowns. He shows how to convert a problem stated verbally into a system of polynomial equations, and then how to reduce the system to a single polynomial equation in one unknown, which he solves by English mathematician William Horner's method using synthetic division. To do this he makes use of the Pascal triangle, which he labels as the diagram of an ancient method. Zhu also found square and cube roots by solving quadratic and cubic equations, and added to the understanding of series and progressions, classifying them according to the coefficients of the Pascal triangle. He also show how to solve systems of linear equations be reducing the matrix of their co-efficient to diagonal form. His methods pre-date Blaise Pascal, William Horner, and modern matrix methods by many centuries. The preface of the book describes how Zhu traveled around China for 20 years as a teacher of mathematics.

 

 

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