Yau travels down the road less taken

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.”