Zhu Shijie courtesy name Hanqing , pseudonym

Pseudonym

A pseudonym is a name that a person assumes for a particular purpose and that differs from his or her original orthonym...

 Songting , was one of the greatest Chinese

China

Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

s lived during the Yuan Dynasty

Yuan Dynasty

The Yuan Dynasty , or Great Yuan Empire was a ruling dynasty founded by the Mongol leader Kublai Khan, who ruled most of present-day China, all of modern Mongolia and its surrounding areas, lasting officially from 1271 to 1368. It is considered both as a division of the Mongol Empire and as an...

.

Zhu was born close to today's Beijing

Beijing

Beijing , also known as Peking , is the capital of the People's Republic of China and one of the most populous cities in the world, with a population of 19,612,368 as of 2010. The city is the country's political, cultural, and educational center, and home to the headquarters for most of China's...

. Two of his mathematical works have survived. Introduction to Computational Studies , written in 1299, is an elementary textbook on mathematics. Zhu included four illustrative problems to explain operations in arithmetic

Arithmetic

Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...

 and algebra

Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

, adding 284 further problems as exercises. This book also showed how to measure different two-dimensional shapes and three-dimensional solids. The Introduction had an important influence on the development of mathematics in Japan

Japan

Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...

. The book was once lost in China until a copy of the book was made from a Korea

Korea

Korea ) is an East Asian geographic region that is currently divided into two separate sovereign states — North Korea and South Korea. Located on the Korean Peninsula, Korea is bordered by the People's Republic of China to the northwest, Russia to the northeast, and is separated from Japan to the...

n source from a reprinted edition of 1660.

Jade Mirror of the Four Unknowns

Zhu's second book, Jade Mirror of the Four Unknowns , written in 1303, is his most important work. With this book, Zhu brought Chinese algebra to its highest level. The first four of the 288 problems for solution illustrate his method of the four unknowns. He shows how to convert a problem stated verbally into a system of polynomial equations (up to 14th order), and then how to reduce the system to a single polynomial equation in one unknown, which he solves by Southern Song dynasty mathematician Qin Jiushao's "Ling long kai fang" method published in Shùshū Jiǔzhāng (“Mathematical Treatise in Nine Sections

Mathematical Treatise in Nine Sections

The Mathematical Treatise in Nine Sections is a mathematical text written by Chinese Southern Song dynasty mathematician Qin Jiushao in the year 1247.This book contains nine chapters:#Da Yan type ;#Heaven phenomena...

”) in 1247 (more than 570 years before English

England

England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...

 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 first discovered by Jia Xian

Jia Xian

Jia Xian was a Chinese mathematician from Kaifeng of the Song Dynasty, in the first half of the 11th century.-Biography:...

 before 1050.
The final equation and one of its solutions is given for each of the 288 problems.
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 showed how to solve systems of linear equation

Linear equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable....

s be reducing the matrix of their coefficents to diagonal form. His methods pre-date Blaise Pascal

Blaise Pascal

Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...

, William Horner, and modern matrix methods by many centuries. The preface of the book describes how Zhu travelled around China for 20 years as a teacher of mathematics.