Shing-Tung Yau

Shing-Tung Yau
Shing-Tung Yau
Born	4 4, 1949
Birthplace	Shantou, Guangdong, Republic of China
Nationality	Chinese-American
Occupation	Mathematician
Title	Director, Yau Mathematical Sciences Center; Professor Emeritus, Harvard University
Employer	Tsinghua University
Known for	Calabi conjecture, positive mass theorem, Monge–Ampère equation, SYZ conjecture, Yau manifold
Education	University of California, Berkeley (PhD, 1971)
Spouse(s)	Yu-yun Kuo
Children	2
Awards	Fields Medal (1982) Crafoord Prize (1994) National Medal of Science (1997)

Shing-Tung Yau (Template:IPAc-en; Template:Zh; born April 4, 1949) is a Chinese-American mathematician whose work has reshaped the landscape of modern differential geometry and geometric analysis. Born in Shantou, China, raised in British Hong Kong, and educated in the United States, Yau has spent more than five decades at the intersection of mathematics and theoretical physics, producing results that have had far-reaching consequences in fields ranging from general relativity to string theory. He was awarded the Fields Medal in 1982 for his contributions to partial differential equations, his resolution of the Calabi conjecture, his work on the positive energy theorem, and his advances on the Monge–Ampère equation. Among the most honored mathematicians of his generation, Yau has also received the Veblen Prize (1981), the John J. Carty Award (1981), the Crafoord Prize (1994), the National Medal of Science (1997), the Wolf Prize in Mathematics (2010), and the Shaw Prize (2023). He served as the William Caspar Graustein Professor of Mathematics at Harvard University for decades before moving to Tsinghua University in Beijing in 2022, where he directs the Yau Mathematical Sciences Center and chairs Qiuzhen College.

Early Life

Shing-Tung Yau was born on April 4, 1949, in Shantou, a coastal city in Guangdong province, in what was then the Republic of China. His family relocated to British Hong Kong when he was young, where he grew up and received his early education. Details of his childhood and family circumstances during this period point to a formative environment shaped by the broader upheavals in mid-twentieth-century China, which saw many families migrate to Hong Kong during the late 1940s and 1950s.

Growing up in Hong Kong, Yau developed an early aptitude for mathematics. He pursued his undergraduate studies at the Chinese University of Hong Kong, where he laid the foundations for what would become a historically significant career in mathematical research. His talent attracted the attention of faculty members who encouraged him to continue his studies abroad.

In 1969, at the age of twenty, Yau left Hong Kong for the United States to pursue graduate studies. This move marked a turning point in his life, placing him within the American academic system at a time when several leading centers of mathematical research were producing groundbreaking work in geometry and analysis.

Education

Yau enrolled at the University of California, Berkeley, for his doctoral studies, where he came under the supervision of the eminent Chinese-American mathematician Shiing-Shen Chern, himself one of the most influential geometers of the twentieth century. Under Chern's guidance, Yau completed his PhD in 1971 at the age of twenty-two, with a dissertation titled On the Fundamental Group of Compact Manifolds of Non-Positive Curvature. The dissertation addressed deep questions in Riemannian geometry concerning the algebraic topology of manifolds with curvature constraints, themes that would recur throughout Yau's subsequent research.

The training Yau received at Berkeley was instrumental in shaping his mathematical approach, which combined techniques from partial differential equations, differential geometry, and algebraic geometry. The intellectual lineage connecting Chern's geometric vision to Yau's subsequent breakthroughs represents one of the most productive mentor–student relationships in the history of modern mathematics.

Career

Early Academic Positions

Following the completion of his doctorate in 1971, Yau embarked on a series of academic appointments at leading American research universities. He held positions at the Institute for Advanced Study in Princeton, Stony Brook University, and Stanford University during the 1970s and early 1980s. These years were extraordinarily productive, as Yau produced a series of results that fundamentally altered the fields of differential geometry and geometric analysis.

Resolution of the Calabi Conjecture

Among Yau's most celebrated achievements is his proof of the Calabi conjecture, which he completed in 1976. The conjecture, posed by Eugenio Calabi in 1954, concerned the existence of certain Kähler metrics on compact Kähler manifolds. Specifically, it asked whether, given a compact Kähler manifold and a prescribed Ricci form representing the first Chern class, there exists a Kähler metric with that Ricci curvature. Yau's proof established the existence of Ricci-flat Kähler metrics on manifolds with vanishing first Chern class. These manifolds subsequently became known as Calabi–Yau manifolds.

The resolution of the Calabi conjecture had consequences that extended well beyond pure mathematics. In the mid-1980s, physicists working on string theory discovered that Calabi–Yau manifolds provided the precise geometric structures needed to compactify the extra spatial dimensions predicted by the theory. This connection between Yau's mathematical work and theoretical physics has remained one of the most notable examples of the interplay between pure mathematics and fundamental physics.

Positive Mass Theorem

In collaboration with Richard Schoen, Yau proved the positive mass theorem (also known as the positive energy theorem) in general relativity. This result, established in stages during 1979 and 1981, demonstrated that the total mass (or energy) of an isolated gravitational system in general relativity is always non-negative, provided the local energy density is non-negative. The theorem resolved a long-standing conjecture in mathematical physics and provided rigorous mathematical justification for a physical principle that had been assumed but not proven. The proof employed sophisticated techniques from the theory of minimal surfaces and geometric analysis, methods that Yau and Schoen had been developing jointly.

The positive mass theorem is considered one of the foundational results in mathematical general relativity and was cited among the principal achievements for which Yau received the Fields Medal.

Monge–Ampère Equation and Other Contributions

Yau made fundamental contributions to the theory of the Monge–Ampère equation, a fully nonlinear partial differential equation that arises naturally in differential geometry, optimal transport, and several other mathematical disciplines. His work on this equation was closely related to his proof of the Calabi conjecture, as the problem of finding Kähler metrics with prescribed Ricci curvature reduces to solving a complex Monge–Ampère equation. The techniques Yau developed for these equations have found broad application in geometric analysis.

Beyond these landmark results, Yau's research has touched upon numerous other areas of mathematics and mathematical physics. His contributions to convex geometry, algebraic geometry, enumerative geometry, and mirror symmetry have each generated substantial bodies of follow-up work by other researchers. The SYZ conjecture, formulated by Yau with Andrew Strominger and Eric Zaslow in 1996, proposed a geometric explanation for mirror symmetry in terms of special Lagrangian fibrations, and it remains an active area of research in both mathematics and string theory.

Yau also contributed to the Frankel conjecture and to the study of the Minkowski problem, among numerous other results. The breadth of his output — encompassing pure geometry, partial differential equations, mathematical physics, and applied mathematics — has been noted as exceptional even among Fields Medalists.

Harvard University

In 1987, Yau joined the faculty of Harvard University, where he was appointed the William Caspar Graustein Professor of Mathematics. He remained at Harvard for over three decades, during which time he built one of the world's leading research groups in geometric analysis. At Harvard, Yau supervised a large number of doctoral students and postdoctoral researchers, many of whom went on to hold prominent positions at major research universities worldwide.

During his tenure at Harvard, Yau also engaged in extensive efforts to promote mathematical research and education in China. He founded several mathematical research institutes, including the Morningside Center of Mathematics at the Chinese Academy of Sciences and mathematical centers at Zhejiang University and other Chinese institutions. He initiated competitions and programs to identify and nurture talented young mathematicians in China, including the Yau High School Science Award.

A 2006 profile in The New York Times discussed Yau's extensive influence in both American and Chinese mathematical communities, as well as controversies surrounding credit for the proof of the Poincaré conjecture and related disputes within the mathematical community.

Move to Tsinghua University

In 2022, Yau left his position at Harvard to join Tsinghua University in Beijing full-time, becoming professor emeritus at Harvard. At Tsinghua, he serves as director of the Yau Mathematical Sciences Center and as chair of Qiuzhen College, an undergraduate program designed to cultivate mathematical talent in China. In a 2025 interview with the South China Morning Post, Yau stated that China was "still far behind" the United States in mathematical prowess but was "on the rise," and that his goal at Tsinghua was to help produce the next generation of leading Chinese mathematicians.

In a January 2026 interview with China Daily, Yau described his educational philosophy at Qiuzhen College: "We aim to cultivate innovative and interdisciplinary talent with passion, not narrow specialists." He has spoken publicly about the importance of mathematics to national technological development, including in a September 2025 interview in which he discussed the role of mathematics in developing advanced technologies.

In October 2025, Yau participated in the World Laureates Forum in Shanghai, where he was among two dozen winners of the Nobel, Turing, Wolf, and Fields awards gathered for exchanges on frontier scientific topics. Yau described the forum as "a venue for profound exchanges between top scientists."

In an October 2025 interview with the South China Morning Post, Yau discussed his views on China's need to "chart its own path" for technological independence, emphasizing the foundational role of mathematics in scientific and technological development.

Epstein Files

In January 2026, newly released U.S. Department of Justice documents related to convicted sex offender Jeffrey Epstein revealed that Yau's name appeared in correspondence concerning a proposal to establish a Tsinghua University campus in Boston. According to reporting by the Harvard Crimson, Harvard alumnus and donor Gerald L. Chan had coordinated with Epstein in late 2016 to explore this proposal, which involved figures affiliated with both Tsinghua and Harvard. MSN reported that Yau appeared in the released files in connection with these discussions.

Personal Life

Yau is married to Yu-yun Kuo. They have two sons, Michael Yau and Isaac Chiu. Yau has maintained connections to both the United States and China throughout his career, holding positions and engaging in academic activities in both countries. He holds membership in the Academia Sinica and has been associated with numerous academic institutions across the world.

Yau has spoken publicly about his upbringing in Hong Kong and his experiences as an immigrant in the United States. In interviews, he has discussed the influence of his doctoral advisor Shiing-Shen Chern on both his mathematical work and his broader approach to fostering international mathematical collaboration, particularly between the United States and China.

Recognition

Yau has received a large number of awards and honors over the course of his career. His most significant recognitions include:

• John J. Carty Award for the Advancement of Science (1981), awarded by the National Academy of Sciences.
• Oswald Veblen Prize in Geometry (1981), awarded by the American Mathematical Society, for his contributions to differential geometry.
• Fields Medal (1982), awarded at the International Congress of Mathematicians, in recognition of his work on the Calabi conjecture, the positive energy theorem, the Monge–Ampère equation, and partial differential equations.
• Crafoord Prize (1994), awarded by the Royal Swedish Academy of Sciences, for his development of nonlinear techniques in differential geometry.
• National Medal of Science (1997), the highest scientific honor bestowed by the United States government, presented by President Bill Clinton.
• Wolf Prize in Mathematics (2010), awarded by the Wolf Foundation in Israel, for his work in geometric analysis and mathematical physics.
• Shaw Prize in Mathematical Sciences (2023).

Yau is a member of the U.S. National Academy of Sciences, the American Academy of Arts and Sciences, and the Academia Sinica in Taiwan. He has received honorary degrees from numerous universities worldwide.

Legacy

Yau's influence on modern mathematics extends through both his own research output and his extensive work in institution-building and mentorship. His resolution of the Calabi conjecture gave rise to the study of Calabi–Yau manifolds, which have become central objects in both algebraic geometry and theoretical physics, particularly in the context of string theory and mirror symmetry. The positive mass theorem, proved with Richard Schoen, remains a cornerstone of mathematical general relativity. His contributions to the Monge–Ampère equation and to geometric analysis more broadly have influenced generations of researchers.

Beyond his direct mathematical contributions, Yau has had a substantial impact on the global mathematical community through his founding of research institutes, his organization of conferences, and his mentorship of doctoral students and postdoctoral researchers. He has been instrumental in building mathematical infrastructure in China, founding centers at Tsinghua University, the Chinese Academy of Sciences, and Zhejiang University, among others. His establishment of Qiuzhen College at Tsinghua University represents his commitment to training the next generation of Chinese mathematicians at the highest international level.

Yau's career, spanning from his doctoral work under Shiing-Shen Chern at Berkeley in 1971 to his current role at Tsinghua, represents a continuous thread connecting twentieth-century differential geometry to twenty-first-century mathematical science and education. His work has been recognized with virtually every major prize in mathematics, and the mathematical structures bearing his name — Calabi–Yau manifolds, Yau's theorem, the SYZ conjecture — remain subjects of active research across multiple disciplines.