Almost all the fifteen chapters of this book have been broadened and enriched, and there are still many improvements, so I won't list them here. Among them, the main improvements are as follows: Chapter 5 discusses the contents of Euclid's Elements of Geometry; The seventh chapter deals with China's mathematics. Chapter 9, dealing with logarithm; Chapter 12 is a brand-new chapter on Agnez and Duchatelle; Chapter 13 talks about the contribution of Agante and wessel to the geometric representation of complex numbers; Chapter 13 adds a new part to germain and Somerville: Chapter 13 adds a new part to Porzano; Chapter 13 significantly expanded the information of geometric liberation in19th century; The part about differential geometry in chapter 14 has been completely rewritten and expanded. 14 supplemented the information about Chisholm and Scott; At the end of this book, a new section is added to predict the future of mathematics.

A major supplement to this book is the Background of Civilization written by Jamie eves. This is written to meet the requirements of early users of this book. They think it will help students to understand the history of mathematics in different times and periods in a deeper cultural background. Smart students should carefully read the cultural background of some chapters before they begin to explore their historical materials.

This book has added 10 pictures and 16 photos of mathematicians. Finally, the references are greatly expanded.