By Diana Steele

The Shape of a Life*Shing-Tung Yau and Steve Nadis**Yale Univ., $28*

One of the first remarkable things that mathematician Shing-Tung Yau reveals in his memoir, *The Shape of a Life*, is that his name was not originally Yau. His family fled China to British-ruled Hong Kong in 1949 when he was an infant, and the name Yau came from a mistranslation on a registration form when he entered elementary school. No one in the family spoke English, so to fill out paperwork, they relied on an English-speaking teacher, who incorrectly translated his family name of “Chiu” to Yau.

At the time, neither Shing-Tung nor anyone in his family thought it mattered. Little did they know that the name Yau would become immortalized in physics and mathematics as half of the Calabi-Yau manifolds, which are geometric shapes that provide mathematical insight into string theory. Yau jokes that these names have become so inextricably linked that he almost believes his first name is Calabi.

*The Shape of a Life*, written with science writer Steve Nadis, traces the remarkable arc of Yau’s life, from poverty and exile in Hong Kong to international renown as a Chinese-American mathematician and the first Chinese winner of the Fields Medal, often described as the Nobel Prize of mathematics. Along the way, Yau encountered many tipping points that changed the trajectory of his life.

His book is filled with reminiscences of childhood in Hong Kong — both tragic and happy — including a charming anecdote of pondering geometric proofs when he was introduced to geometry in middle school. “I was amazed to see how far one could go, and how many theorems one could prove, starting from five simple axioms,” he writes. “For some reason, which I couldn’t quite put into words at the time, that idea made me happy.”

Points at which he could have faded into obscurity — leading a gang in petty crime as an 11-year-old, and his father’s death when Yau was only 14, which plunged the family deeper into poverty — are contrasted with his remarkable luck. At 19 he was perhaps luckiest of all, coming under the wing of China’s undisputed emperor of mathematics, Shiing-Shen Chern. Chern mentored Yau in graduate school at the University of California, Berkeley, which Yau attended despite not having yet finished his undergraduate degree in Hong Kong. He completed his Ph.D. in two years and launched a career that included over 30 years as a professor at Harvard University.

Yau’s foundational research in geometric analysis knit together the fields of topology and theoretical physics. His Fields Medal was awarded in 1982 for his proof of Italian-born American mathematician Eugenio Calabi’s conjecture describing the special properties of a large class of multidimensional geometric forms, or manifolds. Yau proved that these higher-dimensional manifolds could exist, allowing physicists to potentially decipher a puzzle that Albert Einstein failed to solve. Einstein never found a unifying theory to explain the fundamental forces of nature. But if the universe contains compact, hidden extra dimensions in the shape of Calabi-Yau manifolds, then string theory may provide a way to reconcile the gravity of general relativity with the quantum scale of particle physics.

Yau’s contributions to mathematics, and especially to the redevelopment of an academic culture of mathematics in China, are themselves manifold. He founded three mathematical institutes in China and has been outspoken about the need to develop a more innovative research culture there.

Yau accessibly conveys complex mathematical concepts. But the narrative occasionally gets bogged down when he discusses political infighting in mathematics, which may seem tiresome to those who have no direct knowledge of the people or events in question, and possibly irritating to those who do.

Ultimately, Yau’s stories about his childhood, overcoming family tragedies and his deep love for mathematics are the threads that engage the reader. The book is enriched by photographs of Yau’s family, along with sketches and photographs of sculptures inspired by Calabi-Yau manifolds. It’s bookended by Yau’s poetry, inspired by his father, a revered figure in Yau’s life even after his early death. In one poem, titled “Ode to Space-Time,” Yau writes:

So immense our puzzling universe appears,

yet how beautiful, inexpressible, the origin of truth is.

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