As-samawal And His The Al-Bahir

In the article we'd like to introduce a distinguished Arabic mathematician As-samawal and his algebra work in 12th century. As-samawal had many mathematical works in his life. His algebra book The al-Bahir which was kept till today is significant in the history of mathematics. This book included Karaji's binomial theorem and rules of the arithmetic polynomial operations and it developed Karaji's theory of polynomial. As-samawal used a simple inductive way which played a important role in establishing mathematical induction in this book. Besides that, the writer understood the rule of negative multiplication completely and he studied the problem of permutation and combination deeply. We can also find some Chinese traditional mathematical problems in the al-Bahir. For instance, the question of Hundred Chickens and "Ying Bu Zu Shu". Because the study of As-samawal and his works is not sufficient in China, the emphasis of this article is to introduce As-samawal and The al-Bahir in detail. By comparing the al-Bahir with other algebra works before it, we can learn the advantage and defect of the book and try to analyze the origin of the writer's mathematical idea.