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Yau: 'Many problems in science and engineering can be turned into mathematical problems.' (Staff photos Stephanie Mitchell/Harvard News Office)

Yau travels down the road less taken

Professor uses math to pursue interest in natural phenomena

By Bob Brustman
Harvard News Office

Horng-Tzer Yau's affinity for mathematics was obvious in high school, where, in his native Taiwan, he began studying advanced calculus and college algebra. He developed an interest in physics at the same time and was intrigued by relativity and quantum mechanics.

At the National Taiwan University, Yau's focus remained on mathematics. It was in Princeton University's doctoral program in the subject that, along with his enchantment for the beauty and clarity of mathematics, Yau became drawn to understand nature as well. That's when he made the decision to forge his own path to the study of natural phenomena through the study of mathematical physics.

Using the language of mathematics, Yau examines, among other heady conundrums, "many-body" and nonlinear problems in nature, including fluid and quantum mechanics. He has used statistical mechanics to interpret descriptive models of physical phenomena on a scale ranging from microscopic to astronomical. Using quantum mechanics, he has described the stability of matter in particle systems like dense gasses, liquids, and solids, yielding mathematical support for earlier astrophysical theories on the limits of stellar stability. Recently, Yau proved that Brownian motion - the physical phenomenon that minute particles immersed in a fluid move about randomly - emerges from a quantum particle in a random environment.

Today, Yau is a professor of mathematics in Harvard University's Faculty of Arts and Sciences, an appointment he has had since last July. His main interests are in the quantum mechanics of many particle systems, probability theory, and partial differential equations. After Newton, he explained, "some of the most successful tools to describe nature are partial differential equations. Most natural phenomena are described by partial differential equations: the weather, materials science, semiconductors, lasers, and general relativity. They are fundamental tools to describe natural phenomena."

Yau continued: "But for systems with many particles, the degree of freedom is huge - there are too many variables - and it is extremely difficult, if it is possible at all, to solve approximately differential equations with such a degree of freedom. For these systems, one has to bring in probabilistic concepts such as the law of large numbers and entropy ... to cast the differential equations into more manageable forms. This is a new direction in partial differential equations that combines traditional analytical tools with statistical concepts.


"My focus is on finding clean, simple, mathematical concepts that help in understanding natural phenomena."

This past fall, Yau taught a graduate seminar on the mathematical theory of quantum electrodynamics. He said he taught the class because he was interested in the recent progress on the topic and also that it's helpful to him to teach graduate courses that are not exactly his primary interest, but its neighbor. Through the interaction with young minds he and his students can both learn something new.

This spring, he is teaching something he knows very well, and that is the undergraduate course "Topics in Analysis," including discussion of differential equations.

Yau comes to Harvard from Stanford University, where he had been a professor of mathematics since 2003. Moving to Harvard appealed to him, he said, because "the Harvard Math Department is probably the most active math department in the world. And the students are the best in the country." And now that he's here, he enjoys the intellectual vitality of the department. "I often spend the afternoon with one or more of my colleagues," he said, "exchanging opinions and thoughts on each other's ideas."

Honors accorded Yau include a Sloan Foundation Fellowship and Packard Foundation Fellowship, both in 1991, and the Henri Poincare Prize and a MacArthur Fellowship in 2000.

Yau still likes mathematics for the freedom it gives him in connecting with other subjects. "Many problems in science and engineering can be turned into mathematical problems," he said. "Not just mathematics and physics, but computer science, biology, finance, image and signal processing. Another thing I like about mathematics is that I can work wherever I am. I can work in the office, or in many other places, because the problems are actually deep in my mind."

And, though it's important to be able to use the heavy machinery of mathematics and to solve complicated problems, he says he takes a special delight in finding simple, elegant methods to probe complex questions.


Copyright 2007 by the President and Fellows of Harvard College