Two track mind

As a double major in French and mathematics, Karen Parshall had the best of both worlds.

“I was really interested in both sciences and the humanities,” she said. “It was a wonderful kind of schedule, because I could — it sounds kind of trite — exercise both sides of my brain.”

As a member of the third fully coeducational class, Parshall (Mathematics, French ’77, MS, Mathematics ’78) worked hard and graduated with highest distinction. “I never darkened the door of a fraternity,” she said. “I’ve always thought of U.Va. as a place where, if you’re really a social type, you have a niche, but, if not, there are enough like-minded people to create your own community.”

She’s back at the University and still making cross-disciplinary connections in her scholarly work. With a dual appointment in mathematics and history, she teaches mathematics courses for majors, the history of mathematics and two classes in the history of science. She also directs the history of mathematics doctoral program.

Her history of mathematics courses begin with the theories of Pythagoras and Euclid; their work defined mathematics for close to 1,600 years. The classes then move through the development of calculus by Newton and Leibniz in the 17th century and continue to explore the “almost exponential” growth of the field since the 19th century, she said.

Her fall semester course on the Scientific Revolution uses primary sources and begins with classical Greek antiquity so students “know what it is the people in the 15th, 16th and 17th centuries were reacting to.” In the spring, Parshall teaches a class on the social history of the development of American science, from the Colonial period to 1950.

She even had a chance to teach in French, in 1985, at the École des Hautes Études en Sciences Sociales in Paris.

What does Parshall like about mathematics? “The challenge of it, the beauty of it, the logic of it, the difficulty of it. And from a historian’s point of view, it’s incredibly fascinating to see how the various historical figures reacted to the environments in which they found themselves and how they pushed in different directions.”

Her initial University of Virginia ties have continued in research supported by the National Science Foundation and the Guggenheim Foundation. She is working on the biography of James Joseph Sylvester, a British mathematician who developed “invariant theory,” an area that became fundamental in 19th- and 20th-century mathematics. Her book of his letters, with extensive historical and mathematical commentary, was published by Oxford University Press in 1998.

Jewish at a time when only members of the Church of England could attend Oxford or receive degrees from Cambridge University, Sylvester studied at Cambridge. Although he couldn’t take a degree, he did take the required final exam. He placed second, “a major mark of distinction in British society” that normally was a ticket to a teaching position at Cambridge, Parshall said. Again, he was barred on religious grounds.

“He then had to craft a career for himself in Britain. In a real sense he’s one of the mid-19th-century scientists who defined the scientific profession” as one based on the production of original research, Parshall said.

Sylvester came to U.Va. for the 1841-42 session, but he arrived when student unrest was high and sentiment against non-American faculty was virulent, both on-Grounds and in newspaper editorials. His pavilion was stoned; he had disrespectful students in his class. When his request that one such student be expelled was denied, Sylvester resigned.

“In the end, he was the first professor of mathematics at Johns Hopkins,” Parshall said, “and started the first graduate-level program in mathematics in the United States. Sylvester provides an almost unique optic for looking at the history of 19th-century science.”