How to Do Good Mathematics

How to Do Good Mathematics presents a rich collection of reflections on mathematics and the life of one of its greatest modern contributors, Shiing-Shen Chern. The book is organized into four parts.

The first part offers a concise biography of Chern along with an overview of his mathematical achievements and philosophy. The second part features ten of Chern's essays, which include his observations on the development of mathematics in China and the world, his vision for vibrant and meaningful mathematics, and his heartfelt advice to young mathematicians. He also emphasizes the importance of integrating humanistic values into the practice of mathematics. The third part consists of conversations with mathematicians such as Zhang Dianzhou and Jackson, touching on the qualities of a mathematician and the relationship between mathematics and science. The fourth part includes four accessible public lectures delivered by Chern, focusing on the evolution of modern geometry and its connection to physics.

Shiing-Shen Chern (1911- 2004) was a pioneering mathematician, widely regarded as the father of modern differential geometry. His work laid the foundation for major developments in global differential geometry, characteristic classes, and their applications in both mathematics and physics.

Born in China, Chern held positions at prestigious institutions including the University of Chicago, Princeton, and UC Berkeley. He was the founding director of the Mathematical Sciences Research Institute in Berkeley and a foreign member of the Chinese Academy of Sciences.