His finalist year: 1963

His finalist project: Trying to show that every even number can be expressed as the sum of two prime numbers

What led to the project: Joel Kugelmass had some interesting reading tastes as a child growing up in the 1950s. He read Euclid's writings on geometry as a 11-year-old seventh grader. (He had skipped grades.) He soon turned his attention to number theory, reading everything he could about this "elegant" branch of mathematics that is concerned with the properties of numbers. This interest was surprising to his more literary family—his father was a reporter at the San Jose Mercury News—but he kept at it.

In high school he did a math project for the Westinghouse Science Talent Search in which he attempted to show that every even number can be expressed as the sum of two prime numbers. (Prime numbers are those including 2, 3, 5, 7, 11,13 and so on that can only be divided without a remainder by 1 and themselves.) For instance, 10 is the sum of primes 7 and 3.

He came up with a fairly imaginative proof of the idea—with one problem: He'd made a mistake, a reality that was pointed out "in the first five minutes of my interview when I got to Washington," D.C., as a finalist in 1963, he says. "It was a difficult way to start, I must admit." But the judges were still impressed with his ability to think on his feet and answer other questions. "I guess I wasn't the first mathematician to have a faulty proof," he says.

The effect on his career: The Westinghouse contest did shape Kugelmass's life, though probably not in the way its founders intended. Like many finalists, before going to college, Kugelmass did a summer math internship at what was then called the National Bureau of Standards, now called the National Institute of Standards and Technology. The year 1963 was a heady time to be in the nation's capital. Kugelmass went to the march on Washington on August 28, and found listening to Martin Luther King, Jr.'s "I Have a Dream" speech to be an "unbelievable experience."

But the next day when he went to the usual lunch spot where the mathematicians he worked with gathered, "there was no discussion about it," he says. "It's like it didn't happen. I think at that point I began to wonder a little bit if these were my kind of people." He started at Stanford University as a math major, but an existential literature class he took sophomore year—in which the professor would weep with emotion over the texts—pushed him over the edge. No one was weeping in math class. He decided to change fields, graduating in 1967 with a degree in English.

This was the height of the Vietnam War era, so, partly to keep his student deferment, and partly to study literature more intensely, Kugelmass started graduate school at Brandeis University in Waltham, Mass. But he became increasingly involved in the antiwar movement, setting up rallies and such. At one point, Kugelmass ripped up his draft card and mailed it in. He was ordered immediately to report for induction, but he wound up being medically ineligible for service.

He drifted away from graduate school, but kept working as a community organizer, working with various groups in Boston on projects including getting African-Americans elected to the local school board, working with street gangs, and serving as an alternate delegate to the 1972 Democratic convention for Shirley Chisholm.

But eventually, having a girlfriend he wanted to marry, "I looked around and realized I needed to get some gainful employment," he says. He spent three years working for the Massachusetts Department of Public Health, and then his wife, a labor organizer, was transferred to California to work for the United Electrical Workers. Because of his political work, Kugelmass wound up being tapped then, in 1975, to be the executive director of the Pacifica Radio Foundation, a listener-supported network with a history of activism. That lasted until 1979: "Internecine warfare eventually claimed my position," says Kugelmass.

But he'd "done a really good job getting Pacifica running sanely," says Barbara O'Connor, the former chair of the California Public Broadcasting Commission, which hired Kugelmass as its executive director after his Pacifica tenure. O'Connor, now a professor of communications at California State University, Sacramento, recalls Kugelmass's tenure as being "a really good time for public broadcasting," in part because of his "entrepreneurial skill set and curiosity." The commission added stations, started regular coverage of California state politics on its public radio stations, found funds for independent producer programming, and demonstrated new technologies. For example, they held the first videoconference run by the state.

The California government eventually disbanded the commission, though. Kugelmass became a telecommunications consultant, and in 1989, landed a job in the University of California, Davis's telecommunications department. There, he was asked to write a policy paper on telecommuting, which was a very "trendy concept" in the early 1990s. He spent so much time researching how it should be done, and how U.C. Davis could implement a broad telecommuting policy, that in 1995 his report eventually became a book: Jossey-Bass published Telecommuting: A Manager's Guide to Flexible Work Arrangements.

What he's doing now: As Kugelmass notes, he's had a "disparate" career. In 1992 he took a job at U.C. Davis's medical center, helping to build their cancer research program. These days, he writes grant proposals, edits manuscripts, and has set up a video conferencing program that community physicians can use to discuss patients with U.C. Davis's cancer specialists.

It's a different path than he might have predicted taking as a young mathematician. "I can't say what would have ensued had I stayed in the field," he says. "My suspicion is that I was tremendously competent intellectually in mathematics, but maybe not necessarily all that creative."

And as it was, the politics of the times meant that he wouldn't have been happy studying math instead of leading marches. "The social changes that were underway then weren't just events people attended," he says. "It was a daily dose of 'What's the latest from Vietnam?' to 'What is the meaning of a relationship between two people?' These were items that were discussed from breakfast to two o'clock in the morning every single day."