This book chooses mathematicians who represent all the international communities which have made outstanding contributions in various fields of mathematics. Selection based entirely on the size of their mathematical skills and their contributions to the development of natural science rather than in accordance with the editor's personal preference. People tend to ignore the contributions of the ancient Chinese mathematicians for the development of human society, and this study will talk about this deficiency. In addition, the book, will not only show the historical status of famous mathematicians, but will also focus on discovers of rising stars emerged. Accordingly, the book also consists of a compiled list of biographies of all the Fields Prize winners, the Wolf Prize winners, the Nevanlinna Prize winners, the Abel Prize winners and the Poincaré Prize winners, in order to help our generations to learn from the lessons so as to promote the development of mathematical research.