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Explorations in Science and Technology

Using Math to Open New Frontiers

Whether it involves solving a 400-year-old problem or understanding neuronal activity in the brain, math at Pitt combines classical and applied mathematics to open new frontiers.

Distinguished University Professor G. Bard Ermentrout, for example, applies nonlinear dynamics to biological problems. His main focus is in the area of mathematical neuroscience, in which he studies the patterns of activity in networks of neurons.

In 2005, Professor Thomas C. Hales astonished the mathematics world by proving Kepler's Conjecture, one of the world's great math problems. Named after the German astronomer-mathematician Johannes Kepler, who postulated it in 1611, Kepler’s Conjecture held that the most space-efficient way to pack solid spheres of equal size was in a pyramid shape, like a stack of oranges in a grocery store.

Sounds intuitively obvious, yet for nearly four centuries no one who tried (including Sir Isaac Newton) would prove it. But Hales—Pitt’s Andrew W. Mellon Professor of Mathematics—had access to tools that his predecessors lacked: powerful computers. He won the American Mathematical Society’s David P. Robbins Prize in 2007 for his proof.

Professors aren't the only Pitt mathematicians who have set the math world abuzz. In fall 2010, a research paper coauthored by Pitt senior Carey Caginalp (A&S’ 11) and his mentor, Professor Xinfu Chen, was accepted by the French Academy of Sciences for publication in its internationally renowned journal—shortly before Caginalp’s 17th birthday. The paper described an application of the century-old Brownian motion theory to a modern area of applied mathematics.

In 1997, Pitt sophomore Ovidu Savin (A&S ’99) outscored more than 2,500 other math students in North America to finish first in the William Lowell Putnam Mathematics Competition, the world’s most prestigious competition for mathematics undergrads. Today an associate professor of mathematics at Columbia University, the Romanian-born Savin focuses on partial differential equations that describe such natural phenomena as heat and wave propagation and elasticity.

Abstract mathematical work like Savin’s can lead to amazing applications. For example, only pure mathematicians were interested in the theory of finite fields until digital communications came along and scientists began using finite-fields theory as a building block for error correction; everyone using a cell phone today benefits. The theory of partial differential equations itself provides the foundation to build algorithms that lie at the heart of modern technological marvels ranging from GPS to the control system in a hybrid vehicle.