It was the late 1960s, and their plan was to float a banner protesting the Vietnam War above JFK Stadium during the annual Army-Navy Game.

So members of Philadelphia Resistance, an antiwar group, contacted William Davidon, an esteemed Haverford physics professor whose opposition to war equaled theirs.

Davidon calculated how much helium the balloons needed, and bought it. He added weights to keep the sign steady.

On game day, Davidon and his friends gathered in the stadium parking lot and used ropes to guide the banner within view of the stands.

It read: Beat Army. Beat Navy. Join the Resistance.

"There was a very loud roar and suddenly the gates opened up and a lot of people came pouring out," recalled resistance member Tony Avirgan. "We just let go of the ropes and started running up Broad Street. And people were chasing us."

The stunt, long remembered by resistance members, was just a taste of what happened when Davidon unleashed his skills for the antiwar movement.

As revealed in a new book last week, the professor masterminded the never-solved break-in of an FBI office in Media in 1971.

That effort exposed the agency's large-scale spying on antiwar groups, coloring the public's view of the FBI and impacting future federal policies.

The burglars mailed to news organizations documents they stole, including one memo that suggested agents should step up their questioning of protesters in a way that "will enhance the paranoia endemic in these circles and will further serve to get the point across there is an FBI agent behind every mailbox."

If the break-in unfolded like a Hollywood movie, Davidon, who died of Parkinson's disease at 86 in November, was an unlikely lead character.

A man who didn't smoke dope or grow his hair long, the married father belied the stereotype of the 1960s protester, as did many of his fellow burglars.

Then 44, Davidon was a professor whose work in math and physics was hailed as brilliant and so groundbreaking an algorithm is now named after him. He liked to solve equations in his head during downtime and took breaks during family parties to be alone.

He also was a staunch pacifist, his opposition to war sown during his late teens when the United States dropped atomic bombs on Hiroshima and Nagasaki. He joined the civil rights movement, and marched in places like Selma, Ala. He flew to Vietnam as a peace activist as the war began to escalate in 1966.

"He was not the kind of cheerleading, rousing leader one might picture," said David Kairys, a Temple law professor who advised some of the burglars, who until this week had never been publicly linked to the crime.

"But it was very clear that he was a brilliant guy," Kairys said. "And there was a deep fire burning inside and the willingness to take enormous risk."

Davidon grew up in Newark, N.J., and earned three physics degrees, including a doctorate from the University of Chicago. While employed at a laboratory in 1959, he began to work on an idea that transformed the field of nonlinear optimization, a way of designing various systems to work as efficiently as possible, said Jorge Nocedal, an engineering professor at Northwestern.

Nocedal said the Davidon-Fletcher-Powell algorithm, as it's now known, had been used by pilots to pick the best flight trajectory to save fuel.

Davidon landed at Haverford in 1961, teaching physics and math for 30 years and living in the community with his second wife, Ann, and their two daughters. (The couple later divorced).

By the time of the burglary, Davidon was well-entrenched in Philadelphia's antiwar movement, aligned with the Catholic Left, a group willing to break into draft board offices to try to stem the flow of troops to Vietnam.

He had been arrested several times for civil disobedience, including outside the Pentagon. He had also broken into draft board offices, and he told Nocedal he once put a sign that said "don't lock" on a draft board door to give him easy access that night.

Betty Medsger, who revealed Davidon's role in her book The Burglary, said it was Davidon's science-driven love of evidence that spawned the idea of breaking into an FBI office. He wanted proof the agency was spying on protesters, something many had suspected.

He quietly approached a diverse group of people, some of whom had joined him on draft board raids. As Medsger wrote, the seven members of the plot included a religion professor, a day-care center worker, a social worker, and a cab driver. Three were parents with young children, including Bonnie and John Raines, a day-care center director and religion professor at Temple University.

Bonnie Raines told The Inquirer only someone like Davidon could have led the operation and persuaded the recruits.

"He wasn't a reckless man," she said. "He was modest. It needed to be done in a quiet way."

The group spent weeks casing the second-floor FBI office at Front and South Streets in Media, learning when police cars were likely to drive by and discovering that the building's front door was never locked.

It was Davidon's idea to plan the burglary for Monday, March 8, 1971, the night of a heavyweight championship fight between Joe Frazier and Muhammad Ali.

Bonnie Raines found out the office lacked a security system by walking in and telling the agent in charge she was a student researching job opportunities for women. Keith Forsyth, a cabdriver and war resister, had spent weeks learning how to pick a lock.

Davidon oversaw the operation from a nearby motel room, keeping everyone calm and confident when Forsyth discovered the lock on the main door to the FBI office was too difficult to pick, Medsger wrote. Forsyth returned and picked the lock of a second, unused door, gaining access to the office. The burglars carted off about 1,000 files.

Patrick Kelly, an FBI agent who worked in the Media office at the time, said Medsger and others had wrongly glorified the burglary and taken it out of context.

Kelly said the office spent most of its time investigating kidnappings and bank robberies, not spying on protesters. But he said the FBI often had good reason to monitor some of them. For instance, he said, he took part in the raid on a commune the FBI believed was hiding Susan Saxe and Katherine Power, two accomplices to a murder and bank robbery in Massachusetts in 1970.

Kelly, now a private investigator in central Pennsylvania, declined to discuss the specifics of the burglary. But he said: "A lot of groups back then were involved in truly criminal activities. [The Media burglars] portraying themselves as [just] antiwar types. In my opinion, they were more."

Davidon and the burglars never took such a risk again.

Sarah Davidon, one of his daughters, learned decades ago about her father's role in the crime. In a 2010 conversation, she said, she asked him whether he regretted it.

He said he didn't, but tears welled in his eyes as he spoke, she recalled.

"He said maybe he didn't consider as thoroughly the impact it would have on his family if he got caught," she said. "But he felt very confident that he would get away with it and that it was the right thing to do."

Editor's Note: A previous version of this story incorrectly stated that Davidon stole helium from Haverford College.