The beauty of pure mathematics

The applicability of the field isn't the only thing that motivates John E. McCarthy

John E. McCarthy, Ph.D., professor of mathematics in Arts & Sciences, is a native of Ireland who has a facile way with stories. He tells them with an engaging Irish accent, and continually provides fascinating insights into science and life that make you see mathematics and the larger world in a way you’d never anticipate.

He is fervent in the belief that mathematics is central to all of science and that society owes much of its advances to mathematics.

John E. McCarthy, Ph.D. (right), professor of mathematics in Arts & Sciences, and Greg Knese, a second-year mathematics graduate student, share a laugh in McCarthy's Cupples I Hall office.
John E. McCarthy, Ph.D. (right), professor of mathematics in Arts & Sciences, and Greg Knese, a second-year mathematics graduate student, share a laugh in McCarthy’s Cupples I Hall office. “John McCarthy has been a whirlwind of energy, enthusiasm and overall excellence in our department,” says Steven G. Krantz, Ph.D., professor of mathematics and department chair.

He offered the conceptual shift from Roman numerals to Arabic, which reached Europe in the 12th century, as a prime example of how mathematics plays a key role in society.

“Imagine doing banking, compounding interest, using Roman numbers,” he said in his first-floor Cupples I Hall office. “Using Arabic numbers is a huge advantage if you want to calculate 3.25 percent over five years.”

He said the development of calculus in the 17th century sparked a revolution in science.

“Calculus spawned the notion that you could not simply observe natural phenomena but you can predict them,” McCarthy said. “This was a big departure from Aristotle, a kind of biologist, really, who thought that all you need do is look around, see what’s there, record it and categorize it. If you see it everywhere, it’s natural and therefore must be right.”

Statistics is yet another realm of mathematics that changed science, medicine and public policy, not to mention baseball players negotiating their salaries following a monster year. McCarthy noted that statistical techniques proved that bad water was the cause of cholera long before the cholera bacillus was identified.

“The development of statistics in the 19th century might have had more of an impact on medicine than the development of antibiotics,” he said. “It brought the realization that when you see only a small number of a sample, then your observation isn’t necessarily accurate.

“Consider the remedy of bleeding, which was used for over 400 years in Western medicine for practically everything. It was done without a second thought until statistics forced medical science to step backward and say, ‘Maybe we had better test.’ This led to enormous advances in medicine.”

Today, mathematics is applied to “anything that has data,” McCarthy said, “which is all of science. The Human Genome Project, for instance, while relying on remarkable biological techniques, has a large mathematical component of extracting exactly the right data out of a large pool of gene sequences.

“Mathematics is about finding patterns. Go back to counting: When you can count to 10 you have a system that works for sheep and stones and money. Once you master this concept of numbers and abstraction, it, like reading, is widely applicable. And when you learn more sophisticated mathematics, it gives you power over very disparate phenomena.”

McCarthy’s field is a kind of analysis called operator theory, which he defines as the study of matrices in infinite dimensional space. It is most directly linked to the heady realm of quantum mechanics, a physics theory involving elementary particles such as the electron that predicts the outcomes of physical experiments in probabilities.

Operator theory is the language of quantum mechanics, which McCarthy calls “a purely abstract theory developed in the beginning of the 20th century out of sheer curiosity. Most math is developed originally out of curiosity and then turns out to have unexpected uses.”

John McCarthy with his wife, Suzanne Langlois, and their children, Myles and Fiona.
John McCarthy with his wife, Suzanne Langlois, and their children, Myles and Fiona.

McCarthy is a pure mathematician who sometimes participates in some applied mathematical problems. He is taken by the elegance and beauty of pure mathematics and is so enthralled with it and happy teaching and researching at the University that he swears if he won the lottery, he’d never give up his job.

“Of course, I ought to start buying lottery tickets if I’m going to have any chance,” he said, smiling. “It’s a wonderful feeling to have a job you truly enjoy doing. When doing research in pure mathematics, one is motivated not by its applicability but by its beauty.

“There is a feeling in the mathematics profession of a sort of unity, and that if you build it they will come. So, you approach your work as an effort to solve something and that will shed a bit more light on all of mathematics, and experience has shown time after time that doing this will be useful for something.”

John E. McCarthy

Title: Professor of mathematics; faculty member since 1991

Other University positions: Vice chair of the mathematics department, in charge of the graduate program, 1996-present; serves as secretary to the Faculty Senate and as faculty representative to the Board of Trustees; member of Faculty Council of Arts & Sciences, 1999-02

Education: B.A., mathematics, first class honors, Dublin University, 1983; M.Sc., mathematics, Dublin University, 1987; Ph.D., University of California, Berkeley, 1989

Family: Wife, Suzanne Langlois, an owner of Kaldi’s café; daughter Fiona, 3-and-a-half, son, Myles, 1

Hobbies: Ultimate Frisbee pickup games in Forest Park; reading novels and nonfiction, especially history

In addition to its use in quantum mechanics, operator theory can be applied to such recognizable problems as automatic pilot design and oil exploration. Control theory is an old engineering discipline, and designing an automatic pilot is a good example of control theory.

In the automatic pilot problem, operator theory facilitates factoring in and allowing for such parameters as turbulence, time, over-and under-corrections and others, that a plane might encounter from one destination to another.

In oil exploration, operator theory helps researchers decode radar or sonar signals sent into different layers of mud, shale and granite and refracted back to find oil deposits.

“Mainly I’m guided by aesthetics, but more and more I’m finding myself interested in applied mathematics,” McCarthy said.

It was his love of pure mathematics that steered McCarthy, the son of two Limerick physicians, away from medicine and into math his freshman year at Dublin University. Ironically, he found mathematics his toughest subject in high school, owing in part to the rigid Irish academic standards that require as many as nine courses a semester.

The mathematics curriculum takes students as far as the equivalent of finishing the first year of college calculus.

“I had intended transferring to a medicine curriculum, but I found that I loved math and physics so much that I wanted to continue, and I never gave it another thought,” he said.

After earning a master’s degree in mathematics at Dublin University, McCarthy was admitted to the University of California, Berkeley. He wanted to return to Ireland after completing a doctorate, but the Irish universities were under a hiring freeze.

Instead he became visiting professor for two years at Indiana University before coming to Washington University in 1991.

McCarthy became a U.S. citizen in 1996. One of many American things McCarthy became fond of at Berkeley was cafés, relaxing or working in them. After moving to St. Louis, he met his wife, Suzanne Langlois, at Kaldi’s, when he looked into the window of the DeMun neighborhood café one day and saw her roasting coffee. She motioned him in and offered him a tour.

He discovered that Suzanne, a former reporter for The Riverfront Times, was co-owner of Kaldi’s, and the two began a relationship that led to marriage in 1999. They have a daughter, Fiona, 3-and-a-half, and son, Myles, 1.

McCarthy teaches a wide swath of undergraduate and graduate courses, never having taught any one course more than twice in his 12 years here. He said there was something of an adjustment coming to a large Midwestern city from a small one.

“I’ve made the adjustment well, getting used to the winters, but I’m not entirely attuned to the summers,” he said, like many St. Louisans. “I try to return to Ireland each summer. I do miss some things, but everyone is nostalgic for the place where they grew up and old friends.

“But I’m very happy here. Washington University is a great university, and the math department is a friendly place. I feel very fortunate.”

McCarthy’s accomplishments and attitude have not been lost on his colleagues.

“John McCarthy has been a whirlwind of energy, enthusiasm and overall excellence in our department,” said Steven G. Krantz, Ph.D., professor of mathematics and department chair. “He is a standout teacher, a world-class researcher and a reliable and hardworking colleague. He has done wonders as the vice chairman for the graduate program.

“John is also respected and admired for his many contributions around campus. Certainly John McCarthy is one of our most valued colleagues.”

The native son of the Emerald Isle, famous for its warmth and congeniality, finds his newer home warmer and more outgoing.

“I’ve found Americans much warmer than Irish people,” he said. “I was struck by how warm and friendly Americans are when I first came to Berkeley.

“Thanksgiving is the best example. It’s my favorite holiday. In my 20 years here I’ve never spent it alone. That’s very special that a people would have a holiday where everyone gathers and shares their gratefulness, and if you don’t have a family, you’re taken in.”