PARIS — The monsters of al Qaeda and the so-called Islamic State probably never will be held to account the way the Nazis were at the Nuremberg Tribunals after World War II. The snarled red tape and convoluted politics of today’s international organizations will frustrate such grand designs for justice, even after the self-proclaimed “caliphate” is reduced to dust on the ground and unread footnotes in history.

But the trial going on at the International Criminal Court in The Hague this week gives us a hint of what can be done, and, indeed, what must be done.

The defendant, Ahmad al Faki al Mahdi, served the branch of al Qaeda in North Africa that very nearly took over all of the nation of Mali in 2012, until French troops intervened. The terrorists’ greatest prize was the ancient city of Timbuktu, al Mahdi’s hometown, and he did everything he could to show he supported his fanatical mentors’ gruesome diktats.

But al Mahdi is not on trial for the amputations, beheadings, torture, and rapes associated with the “holy war” waged by al Qaeda, ISIS, and their offshoots.

Al Mahdi is on trial for massacring history.

We have seen a lot of savage iconoclasm over the last 15 years. In 2001, the Taliban brought down the towering twin statues of Buddha in Bamayan, Afghanistan—a prelude to the operation by their allies in al Qaeda, who brought down the twin towers of the World Trade Center in New York only a few months later.

More recently we’ve seen the devastation wrought by ISIS on the ancient monuments of Nimrud in Iraq, and those of Palmyra in Syria: winged bulls turned to gravel with jackhammers, the Temple of Baal erased from the map with high explosives.

These would-be holy warriors claim to have a direct line to God, a unique and exclusive understanding of His Truth. They are determined to destroy anyone and anything that does not fit their view, and they do all this in the name of Islam.

So it is worth noting that al Mahdi is on trial, specifically, for leveling the mausoleums of Muslim saints in a city that was one of the cradles of Islamic civilization, and that the prosecutor who leveled the charges against al Mahdi in court on Monday, Fatouh Bensouda, is a Gambian woman from a large Muslim family. She knows where this guy is coming from, which may account in part for the power and passion of her opening statement.

This trial, said Bensouda, is about answering “the destructive rages that mark our times, in which humanity’s common heritage is subject to repeated and planned ravages.”

The mausoleums al Mahdi destroyed were “the embodiment of Malian history, captured in tangible form, from an era long gone yet still very much vivid in the memory and pride of the people who so dearly cherished them.”

“Your honors,” Bensouda told the judges, “culture is who we are.”

Bensouda has been criticized for failing to make the ICC a new Nuremberg. But the criteria she has to work with are suffocating and contradictory.

The court has no jurisdiction over territories where the government is not a party to the Rome Statute that established the court in 1998. So the court has no territorial jurisdiction over the ISIS heartland that straddles Iraq and Syria, neither of which signed on.

The UN Security Council can refer cases, but the United States is not a party to the statute, and neither are Russia and China. That’s three of the five members. The United Kingdom, which did sign on, has discovered that its soldiers are the only people being investigated for crimes in Iraq, even now. (Some in the U.K. would like to see former prime minister Tony Blair charged, but that hasn’t happened.)

Theoretically, individuals can be brought before the court if they are from countries that are parties to it. ISIS has recruits who fit that criterion who are from France, the U.K., Germany, Belgium, the Netherlands, and Austria, among other countries. But the court is supposed to limit its actions to “those most responsible for mass crimes,” as Bensouda declared in April, and since “ISIS is a military and political organization led by nationals of Iraq and Syria,” that limits her ability to pursue them.

Al Mahdi’s case, however, was handed over to the court by the Malian government after al Mahdi was arrested in neighboring Niger last year, and it fits all the narrow criteria. Mali is a party to the Rome treaty, al Mahdi is a Malian citizen, and he was the head of the Hisbah, the “morality brigade” that went on a destructive rampage in Timbuktu for 10 days in June and July of 2012.

The depth and importance of the culture there, and the threats to it under jihadist rule, are the subject of Joshua Hammer’s recent book The Bad-Ass Librarians of Timbuktu. He sees the al Mahdi case as “an important breakthrough and symbol to both the jihadis and their beleaguered subjects that these kinds of crimes won’t go unanswered.”

“To be sure, there’s an argument to be made that the court should be channeling its resources in pursuit of those who stoned adulterers to death and chopped off hands and feet,” says Hammer, but this case “reminds the world that the destruction of cultural patrimony has been one of the jihadists’ most brutal and effective means of intimidating, demoralizing, and breaking the spirits of the people whose lands they occupy.”

As Bensouda put it, “To intentionally direct an attack against historic monuments and buildings dedicated to religion constitutes a war crime” and is “a profound attack on the identity, the memory and, therefore, the future of entire populations.”

We do not know how often Bensouda talked this way to al Mahdi before the trial, but this much we do know. When he stood before the court on Monday, he admitted his guilt.

“I would like to seek the pardon of the whole people of Timbuktu,” said al Mahdi. “I would like to make them the solemn promise that this was the first and the last wrongful act that I will ever commit. I seek their forgiveness.”

Even with his admission of guilt, he is facing many years in prison.

“I am pinning my hope on the fact that the punishment meted out to me will be sufficient for the people of Timbuktu, and Mali, and mankind to offer forgiveness,” he said.

Perhaps they will. But in the meantime the masons of Timbuktu have been hard at work. They are "considered to be 'living human treasures' for their unique craftsmanship," Bensouda told the court. They have rebuilt the mausoleums, while the sculptors of winged lions at Nimrud and the builders of temples at Palmyra are gone forever.