WASHINGTON >> The brothers who carried out suicide bombings in Brussels last week had long, violent criminal records and had been regarded internationally as potential terrorists. But in San Bernardino, California, last year, one of the attackers was a county health inspector who lived a life of apparent suburban normality.

And then there are the dozens of other young American men and women who have been arrested over the past year for trying to help the Islamic State. Their backgrounds are so diverse that they defy a single profile.

What turns people toward violence — and whether they can be steered away from it — are questions that have bedeviled governments around the world for generations. Those questions have taken on fresh urgency with the rise of the Islamic State and the string of attacks in Europe and the United States. Despite millions of dollars of government-sponsored research, and a much-publicized White House pledge to find answers, there is still nothing close to a consensus on why someone becomes a terrorist.

“After all this funding and this flurry of publications, with each new terrorist incident we realize that we are no closer to answering our original question about what leads people to turn to political violence,” Marc Sageman, a psychologist and a longtime government consultant, wrote in the journal Terrorism and Political Violence in 2014. “The same worn-out questions are raised over and over again, and we still have no compelling answers.”

When researchers do come up with possible answers, the government often disregards them. Not long after the attacks of Sept. 11, 2001, for instance, Alan B. Krueger, the Princeton economist, tested the widespread assumption that poverty was a key factor in the making of a terrorist. Krueger’s analysis of economic figures, polls, and data on suicide bombers and hate groups found no link between economic distress and terrorism.

More than a decade later, law enforcement officials and government-funded community groups still regard money problems as an indicator of radicalization.

When President Barack Obama announced plans in 2011 to prevent homegrown terrorism, the details were sketchy, but the promise was clear. The White House would provide warning signs to help parents and community leaders.

“It’s going to be communities that recognize abnormal behavior,” Denis McDonough, the deputy national security adviser at the time, said. As an example, he cited truancy, which he said was an indicator of possible gang activity. “Truancy is also going to be an early warning sign for violent extremism,” he said.

But the years that followed have done little to narrow the list of likely precursors. Rather, the murky science seems to imply that nearly anyone is a potential terrorist. Some studies suggest that terrorists are likely to be educated or extroverted; others say uneducated recluses are at risk. Many studies seem to warn of the adolescent condition, singling out young, impatient men with a sense of adventure who are “struggling to achieve a sense of selfhood.”

Such generalizations are why civil libertarians see only danger in government efforts to identify people at risk of committing crimes. Researchers, too, say they have been frustrated by both the Bush and Obama administrations because of what they say is a preoccupation with research that can be distilled into simple checklists, even at the risk of casting unnecessary suspicion on innocent people.

“They want to be able to do things right now,” said Clark R. McCauley Jr., a professor of psychology at Bryn Mawr College who has conducted government-funded terrorism research for years. “Anybody who offers them something right now, like to go around with a checklist — right now — is going to have their attention.

“It’s demand driven,” he continued. “The people with guns and badges are so eager to have something. The fact that they could actually do harm? This doesn’t deter them.”

Europe, too, is grappling with these questions, but there is no clear answer. Hans Bonte, mayor of the Belgian town of Vilvoorde, attended a White House summit meeting on radicalization last year and described efforts to stem a steady tide of angry young men leaving to join the Islamic State. In Britain, the government encourages or requires people to alert the authorities about people who could become risks. That has spurred debate abroad, and has raised questions in the United States about whether the Constitution would allow the government to keep tabs on lawful political or religious speech.

“I understand, from an American standpoint, that can be troubling,” said Lorenzo Vidino, director of the Program on Extremism at the Center for Cyber and Homeland Security at George Washington University. “But the European model, for most countries, is to intervene early, as soon as you see the first sign of extremism.”

Researching terrorism is admittedly difficult. It involves tough questions about who qualifies as a terrorist, or as a rebel or a soldier. Nelson Mandela? Palestinian suicide bombers? The Taliban of today? The Afghan mujahedeen when the CIA supported them?

Researchers seldom have access to terrorists, and scientific methods, such as control groups, are rare. In 2005, Jeff Victoroff, a University of Southern California psychologist, concluded that the leading terrorism research was mostly just political theory and anecdotes. “A lack of systematic scholarly investigation has left policymakers to design counterterrorism strategies without the benefit of facts,” he wrote in The Journal of Conflict Resolution.

When the government does give advice about what to look for, the origin of that information is often impossible to know. A 2012 National Counterterrorism Center report, for instance, declared that anxiety, unmet personal needs, frustration and trauma helped drive radicalization. “Not all individuals who become radicalized have unmet personal needs, but those who do are more vulnerable to radicalization,” the document said, citing no sources.

In Montgomery County, Md., a Washington suburb, a Muslim-led interfaith organization called Worde thinks it may have a solution. Organizers have provided families and faith leaders with lists of warning signs: depression, trauma, economic stress and political grievances. Anyone who spots these indicator signs can call Worde, which will arrange mental health or religious counseling.

Police officers become involved only when there is a threat of imminent danger, said Hedieh Mirahmadi, the group’s president. Ideally, she said, people get help without being stigmatized or placed on government watch lists.

The program is unproven; a nearly complete study on its effectiveness gives it high marks for building community relationships but does not assess whether the group reduces violent extremism. And while Mirahmadi said “nobody would disagree” with her warning signs, researchers are far less certain that they are indicators of potential radicalization. Still, the Obama administration believes Worde could be a model and has awarded it $500,000 in grants.

Faiza Patel, a lawyer with the Brennan Center for Justice, remains skeptical. Worde has not released its intervention protocols or its method for assessing things like political grievances. Mirahmadi said such tools would be too easily misunderstood.

But, she said, it is a start. She said her group had counseled about 20 people, providing help that otherwise did not exist. Whether any of these people would have become violent, she said, is impossible to know.

© 2016 The New York Times Company