Pope Francis belongs to the Jesuits, a religious order whose members take an unusual — and at the moment seemingly ironic — vow: not to strive for a higher office.

The Jesuits’ culture of modesty and self-effacement has been on full display in recent days, with Catholics worldwide regaled by reports that the new pope had opted to take the bus back from the Sistine Chapel with the other cardinals, and then stopped by his hotel to pay his tab.

For many Jesuits, the concept of one being at the helm of the Catholic Church has required some mental gymnastics.

“I’m in shock that we have a Jesuit pope. This is just not our mind-set. We don’t look for these kinds of offices,” the Rev. Thomas Smolich, president of the Jesuit Conference of the United States, said Friday. “The idea that — it blows the mind.”

The largest Catholic order, the Jesuits were founded by Saint Ignatius of Loyola, a 16th-
century Spanish warrior-turned-priest. In recent decades, they have made building up their network of schools in Latin America and India a top priority, but for centuries their base had been high-quality universities in Europe and the United States, including Washington’s Georgetown University.

Popes from religious orders

Within the confines of Catholicism, Jesuits are generally seen as left-leaning and have burnished a reputation as questioning intellectuals who are open to debate. They are famous for the intensive education they undergo (it can take a decade to become a Jesuit), their required month-long silent retreats and their theology of “finding God in all things.” That idea has attracted progressives but turned off some conservatives who think it sounds relativist.

Strict adherence to doctrine is not typically a focus of Jesuits, and Jesuit institutions are magnets for Catholics who disagree openly with church orthodoxy on issues such as celibacy or female priests. But neither do Jesuits tend to rally publicly against church teaching.

Politically speaking, Francis is an atypical Jesuit. As a cardinal in Argentina, he led a public fight against same-sex marriage — reportedly after failing to broker a deal supporting civil unions — and has said that gay adoption is a form of discrimination against children.

There are no data on whether the typical Jesuit disagrees with the new pope (and official church teaching) on matters such as gay marriage. But questioning a Jesuit on hot-button sexual topics usually elicits a nonjudgmental response.

“We are called to encounter Christ in the people we meet. The typical Jesuit starting point is the experience of people,” Smolich said. “Out of that, we might be more nuanced or more sensitive or more compassionate, in terms of how various church teachings are experienced by people in the pews.”

On the other hand, the new pontiff’s emphasis on uplifting the poor and marginalized is very much in keeping with the Jesuit mission: They take a vow of poverty and have been focused in recent decades on Latin America, home to the world’s largest economic inequality gap.

“Jesuits are supposed to take our vows of poverty seriously,” the Rev. Jim Martin, a former corporate financier who appears frequently on “The Colbert Report,” wrote Thursday, noting that Saint Ignatius of Loyola said we should love poverty ‘as a mother.’ ”

Catholics around the world — including alumni of Washington’s Jesuit-run institutions, such as Georgetown, Georgetown Preparatory School and Gonzaga College High School — are jamming Facebook with excited retellings of how the new pope declined to sit on an elevated platform.

“It’s a very human face to a pope, for people of my generation. We haven’t experienced that,” said Andy Pino, 36, a graduate of Georgetown University. “That is a very Jesuit thing, to be engaged in this way.”

At times, the Jesuit inclination to question things has led the order to challenge authority, most notably in Latin America, and in the views of some, to become too political.

The Vatican shut the order down for several decades in the late 1700s because of the perception that its members were meddling in colonial politics. In the 1980s, the Vatican took the Jesuits over briefly amid concern that members of the order in Latin America were becoming too close to revolutionary groups.

Last week, Catholics were sifting through reports about Francis’s activity during the right-wing Argentine dictatorship in the 1970s and ’80s, known as the “dirty war.” The new pope has been accused of failing to speak out aggressively for victims.

Another, perhaps more familiar, impression in Latin America of Jesuits comes from a famous story of six Jesuits slain in 1989 by the military in El Salvador, where the priests were working against policies they considered oppressive to the poor.

But this week, Jesuits were working to put the stereotypes in context.

Ambivalence about speaking out was typical of mainstream Argentine culture at the time, said the Rev. Matthew Carnes, a Georgetown government professor. He said the Vatican had a point in the past when it worried about Jesuit political activism.

“We Jesuits talk about balancing faith and justice, and maybe there was too much emphasis on justice and not enough on faith,” he said.

Smolich put it more bluntly.

“The days of being sort of bomb-throwers are over,” he said. “We’re not the Democratic Party without the abortion plank. We’re not the loyal opposition.”

In addition to the assumption of authority, there is another irony to the rise of a Jesuit to the papacy in 2013: In many parts of the world, the order is disappearing. Thirty years ago, the biggest regions for Jesuits were the United States, Europe and Latin America. Their numbers have plummeted in all three places.

Jesuit demographics resemble more general demographics in the Catholic Church: a boom in membership after World War II, then a decline starting in the 1970s, and then a small, recent rise. Jesuits’ numbers are shrinking in the same places the number of priests in general is shrinking — in the developed world — and growing where the church is growing, primarily Africa and Asia.

But religious orders such as the Jesuits and the Dominicans are seeing a sharper decline than are priests attached to dioceses.

Hope was widely voiced this past week that Francis’s humble and engaging style and his vigorous stance against global poverty and income inequality would revitalize the Catholic faith and bring its factions together around a common goal.

“He is really focused on the preferential treatment for the poor, which is an area, no matter what your angle is on other things, we are all unified behind, so I hope we can focus on that,” said Pino, the Georgetown graduate, who is gay and opposes church teaching on sexuality. “I’m just hopeful at this point that he’s open to meeting with people, to hearing people’s stories.”

Elizabeth Tenety contributed to this report.