The news that confronts Americans about the decade-long counterterrorism campaign defining the post-9/11 era is increasingly episodic, and for good reason. The death of Osama bin Laden, the killing of Anwar al-Aulaqi, questions about Pakistan’s commitment to the grisly operations against militants in that devastated country — all these are overshadowed domestically by debt problems, a looming election, global warming and a host of other issues worthy of national debate. And they come after a decade in which the number of Americans killed in terrorist attacks is far lower than any observer could have guessed 10 years ago. Americans’ attention has shifted from terrorism, thankfully, and that shift should gratify any security professional.

The popular perception that these terrorists’ deaths mark an accelerating decline among the terrorist groups that threaten the United States, particularly on its home shores, represents an accurate view that the leadership of these groups is disappearing at a remarkable rate. The professionals working against these groups day to day could not help but view the loss of so many al-Qaeda leaders in the border region of Pakistan, the setbacks of the al-Shabab militants in Somalia, the decimation of the al-Qaedist jihadists in Indonesia and the criminalization of hostage-taking al-Qaeda sympathizers in North Africa as signs that the flow of violent Islamist groups that grew after 9/11 has ebbed.

For those of us sitting in a chair at the nightly meetings with CIA Director George Tenet in 2002 and the years afterward, however, the view was not so rosy. Attacks across the Islamic world seemed to represent not only the hydra-headed operational capabilities of a loose, far-flung al-Qaedist movement but also the success of an ideology that led so many formerly local jihadists to go global, accepting the al-Qaeda mantra that the United States and its allies represented the head of the snake. The successes of recent years have erased the sense, during those days, that it was the jihadists on the offensive, while we played defense. No more.

But this same episodic focus — occasional stories marking the decline of various individual leaders — masks a reality that Americans struggle to face: This adversary is not a group, nor is it represented by any individual. It is an ideology, the corrupting vision that American military, cultural and political invasions into Muslim lands must be countered and that the use of indiscriminate violence is an appropriate counter. The Abu Ghraib photos, U.S. policy toward Palestine, photographs of atrocities in Iraq and Afghanistan — all these have fed the belief among the fringe who represent potential al-Qaeda recruits that the United States represents a threat, in their own homelands.

This idea, that youth led by corrupt leaders should turn to al-Qaeda as an answer, had great resonance a decade ago, when al-Qaeda was seen as having stood up to America, and before this decade, during which al-Qaeda operations have killed many innocent Muslims in the Middle East, South and Southeast Asia, and Africa. These killings have radically undercut the appeal of this idea, and the Arab uprisings this year have replaced a recruiting tool for al-Qaeda by ousting unpopular leaders. But these events have not destroyed al-Qaedism. Not yet.

There have been more arrests of al-Qaedist Americans in the past few years than ever before. These people are on the West Coast and the East Coast, in the South and the Midwest, all with their own homegrown plots, coming at us at a rate that we did not see when I first shifted to the FBI from the CIA in 2005. Very few of these individuals are al-Qaeda members; all, though, have absorbed al-Qaedist ideology. They are believers, not recruits. And their numbers have unmistakably increased.

We may be right in looking at reports of the deaths of jihadist leaders overseas as representing a death knell for some of the most significant groups that have threatened America. U.S. military, intelligence and law enforcement operations have combined, with foreign partners, to eviscerate these groups more effectively than we would have expected, even a few years ago.

We would be wrong, however, in confusing the demise of a few leaders or their formal groups with the death of the ideology they sought to spread or the revolution they still intend to inspire. Witness the arrests in this country and the arrests in Europe. Al-Qaedism isn’t close to dead yet. Ideas live far longer than people, and this idea has proven roots. The adversary we face benefits from a long view, looking at the world through a lens of decades or centuries.

We will want to mistake the deaths of al-Qaeda leaders with the death of an ideology. But in the midst of unmistakable successes, we have to match our adversaries by learning to be as patient as they are. Celebrations, or even premature judgments about our successes, would be a mistake. We are far from finished with al-Qaedism, even if al-Qaeda fades.

Philip Mudd served as deputy director of the CIA’s Counterterrorist Center from 2003 to 2005 and later as a senior intelligence adviser at the FBI. He is a senior global fellow at Oxford Analytica, a global analytic and advisory firm.