I was born in Shantou, a small town in southern China in 1949. Before long, my father Chiu Chin Yin brought the family to Hong Kong to flee the civil war, where I grew up in the farming villages in the New Territories.
My father earned his living by lecturing in several colleges simultaneously. The income was meagre and life was hard. Being a traditional scholar, he had high expectations for his children. From an early age I was taught literature and history. I was asked to recite poems and practise calligraphy regularly. This early training sparked my interest in literature and history lasting for a lifetime. My father would gather students at home to discuss various issues on Chinese and Greek philosophy. Although their discussions were far beyond my grasp, those abstract notions deeply impressed me, and had a direct bearing on my future interest in mathematics.
I went to Pui Ching Middle School, a secondary school famous for science subjects. In Grade 8 we learned Euclidean geometry. I was amazed to find that so many beautiful and ingenious results on triangles and circles can be deduced rigorously from five axioms. I indulged myself in the subject and even started my own research on it.
Life was peaceful until my father became sick and died suddenly in 1963. My family ran into financial crisis. However, due to my mother’s persistence, I was able to continue my education. I was admitted to the Chung Chi College, CUHK in 1966 majoring in math. My performance in class caught the attention of Dr Stephen Salaff from Berkeley. Upon his recommendation, I was admitted to the Graduate School in UC Berkeley in 1969.
My first achievement in mathematics, carried out in my first year at Berkeley, to extend a theorem of Preissman on negatively curved manifolds to non-positive ones. My supervisor, Professor S. S. Chern later suggested it to be my thesis. I graduated in 1971.
In 1954, Eugene Calabi proposed to find Kähler manifolds within a Chern class. Although his motivation was purely geometric, I realized that it had important implications in general relativity. Calabi’s conjecture boils down to solving a fully nonlinear partial differential equations (PDE). With much effort, I finally solved the conjecture in 1976. Subsequently, I solved the positive mass conjecture in general relativity with my student R. Schoen using minimal surfaces. Mainly due to these works, I was awarded the Fields Medal in 1982.
Geometric analysis is a new branch of mathematics in which nonlinear PDE’s areemployed to solve problems in geometry and physics. I am considered to be one of its creators. A remarkable achievement in this area is the Ricci-flow proof of the Poincaré conjecture by R Hamilton and G Perelman in 2002. Today, geometric analysis remains as an active research area.
String theory was developed in the 1980’s to unite quantum mechanics and general relativity. It turned out that the Kähler manifolds found in my resolution of the Calabi’s conjecture is precisely the “universe” that physicists were looking for. The “Calabi-Yau space” has become the setting for string theory and its extension. Calabi posted his conjecture purely for its beauty in mathematics, and eventually it has found application in physics. This was a most fulfilling experience for me.
In 1990 my postdoc Brian Greene, and Ronen Plesser, discovered a way to construct a Calabi-Yau space out of a given one so that they both share a hidden kinship. This phenomenon is called “mirror symmetry”. Next P Candelas et al exploited mirror symmetry to solve a century-old problem in enumerative geometry. To explain mirror symmetry, A Strominger, E Zaslow and I proposed the SYZ conjecture.
I held permanent positions at Stanford, IAS Princeton, UC San Diego, and settled at Harvard in 1987. I joined Tsinghua University in 2022. When I was a child, my father told me that one should do something for his own people. I have a long association with the math community in China. Several research institutes were founded by me in Beijing, Hangzhou, Hong Kong and Taipei. A most recent endeavour is the establishment of Qiuzhen College at Tsinghua where gifted high school students are admitted and trained to be leaders in mathematics and basic sciences. I am deeply indebted to the authority and Tsinghua for their enthusiastic support.
I am honored to be awarded the Shaw Prize. Among many awards and honors I have received, the Shaw Prize is a special one, for it is from the city I grew up in and my alma mater. I would like to thank my father for setting a goal of high standards for me, and my mother for showing me how to handle hardship in life. I thank my wife and my two sons for their love and support. I treasure the joy of growing up together with my siblings and childhood friends S T Chui and S Y Cheng. I am indebted to my teachers S S Chern, Charles B Morrey, Louis Nirenberg and I M Singer who taught me ways of thinking mathematics. I thank Richard Schoen, Leon Simon, Karen Uhlenbeck, Nigel Hitchin, Richard Hamilton, David Mumford, Blaine Lawson, Peter Li, Clifford Taubes, Wilfried Schmid, Simon Donaldson, Dimitris Christodoulou, Robert Bartnik, Andy Strominger and Cumrun Vafa, all of whom have influenced my work.
12 November 2023 Hong Kong