# Stephen Smale

# Stephen Smale

**1930-**

**American Mathematician**

The work of Stephen Smale has focused on a number of topics, including topology and dynamical systems. During the 1970s, he turned his attention to the application of mathematical theory to economics, and, in later years, he explored questions in computer science and their application to principles of mathematics. Recipient of the Fields Medal in 1966, Smale has also been honored with the Veblen and Chauvenet prizes.

Smale was born on July 15, 1930, in Flint, Michigan, to Lawrence and Helen Smale. He later described his father as an "armchair revolutionary," who had been expelled from Michigan's Albion University for publishing a radical newsletter. Following his expulsion, Lawrence Smale had gone to work as an assistant in the ceramics laboratory at the AC Spark Plug factory in Flint, the home of General Motors.

When Smale was five years old, his family moved to a small farm outside of Flint, and soon afterward he began his education in a one-room schoolhouse. By the time he was in high school, Smale's interests included chemistry—the field in which he intended to work—and politics. Like his father, he was a student radical, but, as he later recalled, his attempts to organize a protest against the omission of evolution from the biology curriculum failed to stir much support.

By 1948, when he enrolled at the University of Michigan, Smale had switched from chemistry to physics as his intended major. When he began doing poorly in physics, however, he gradually shifted his focus to mathematics, a subject in which he had always excelled. Still, physics was the subject in which he earned his B.S. degree in 1952, and he went on to earn an M.S. in physics the following year. His political radicalism increased during his college years; Smale joined the American Communist Party and protested U.S. involvement in the Korean War. Later, he admitted that his greatest motivation for staying in college during this period was to avoid the draft.

In 1955 Smale married Clara Davis, a classmate at the University of Michigan. The couple later had two children: Laura, who became a biological psychologist, and Nat, who became a mathematician. Smale earned his Ph.D. in mathematics in 1956 and for a period of many years focused on the area of topology, work which earned him the Fields Medal 10 years later. In the meantime, however, Smale had turned from topology to dynamical systems. (The term "dynamical systems" refers to methods for mathematically describing changes that take place over time in some real or abstract system.) Smale's shift in attention to dynamical systems coincided with his acceptance of an appointment as professor of mathematics at Columbia University.

Ever restless, however, Smale experimented with a number of mathematical fields, including the calculus of variations and infinite dimensional manifolds, during the early 1960s. In 1964 he took a position as professor of mathematics at the University of California at Berkeley, and there he began concentrating once again on dynamical systems. At one of the nation's leading centers for the student protest movement of the 1960s, Smale worked with student activist Jerry Rubin and others, organizing and leading protests against the Vietnam War.

As the 1960s became the 1970s, however, Smale began to change both his mathematical interests and his politics. The awarding of the Fields Medal in 1966 had taken place in Moscow and Smale had several other opportunities to visit the Soviet Union, experiences that led to his becoming highly disillusioned with Communism. Eventually, he adopted a stance that he has described as radical in some regards, conservative in others—but always anti-military. As for his professional focus, he turned to mathematical applications in economics, the result of several conversations with Nobel economics laureate Gerard Debreu.

With the explosion of knowledge that took place in the field of computer science during the 1980s, Smale has increasingly turned his attention to that area. He has observed that if the mathematics used in computer science could be brought into closer relationship with mainstream mathematics, revolutionary changes within the discipline of mathematics itself could result.

**JUDSON KNIGHT**

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**Stephen Smale**