After President Obama announced his plan to destroy the Islamic State in Iraq and Syria (ISIS), one general involved in war planning called the mission "harder than anything we've tried to do thus far in Iraq or Afghanistan," according the Washington Post. Given how tough those wars have been for the United States, that's an incredibly high bar. So what is it about the ISIS situation that makes it so very hard for the United States to solve?

Obviously, there are quite a few things that make the crisis in Iraq and Syria complicated. But there are three really important features of the ISIS crisis that make it especially complicated. Each can be represented, simply, in one number. So here are three numbers that explain the ISIS crisis — and why it's so, so difficult to resolve.

1) 20,000

The CIA estimates that ISIS has a fighting strength of 20,000 — at minimum. The high-end estimate is 31,500.

Back in June, the Agency estimated that ISIS topped out at about 10,000 soldiers. But after its June 10 offensive that swept northern Iraq (explained in the above video), ISIS' recruiting surged. Moreover, the group captured advanced American equipment during the offensive, which has given it an edge even against the well-trained Kurdish peshmerga.

These ISIS fighters are extremely effective in tactical terms. The veterans are battle-tested from years of fighting in Syria and Iraq, and ISIS has skilled ex-Saddam commanders in its officer corps. In June, 800 ISIS fighters sent 30,000 Iraqi army troops packing from Mosul, Iraq's second largest city.

Contrast this with the Syrian rebels the US is trying to arm and train. The BBC reported in December 2013 that there are about 1,000 rebel groups in Syria, totaling about 100,000 soldiers. However, that count included not just the rebels that Obama wants to arm and train to fight ISIS, but also ISIS itself, al-Qaeda in Syria, and other jihadi groups.

"the concept of the Free Syrian Army as a unified force with an effective command structure is a myth"

As the Times explains, the prospects for marshaling a unified rebel front against ISIS are dismal at best. "Analysts who track the rebel movement say that the concept of the Free Syrian Army as a unified force with an effective command structure is a myth," the New York Times' Ben Hubbard, Eric Schmitt, and Mark Mazzetti wrote. "Since pushing ISIS from parts of northern Syria early this year, Syria's rebels have few military advances to point to and in many areas have lost ground, to [Syrian dictator Bashar al-]Assad's forces and to ISIS."

"In many places they remain busy fighting Mr. Assad and are not eager to redirect their energies to ISIS," they dourly conclude.

2) 56

New Iraqi Prime Minister Haider al-Abadi's cabinet is 56 percent Shia, according to a count by indispensable Iraq blogger Joel Wing. That makes his cabinet even more Shia heavy than either of his disgraced predecessor Nuri al-Maliki's last two administrations, which were (respectively) 52 and 46 percent Shia.

Why does this matter? Well, Sunni discontent with Iraq's largely Shia government is the core driver of ISIS' strength in heavily Sunni northwest Iraq. The Obama administration's Iraq strategy is premised on the idea that the current government will govern in a far less sectarian manner than Maliki, who was quite cruel to Sunnis, did.

"the new government is likely to be more hardline than Maliki"

"I've insisted that additional US action depended upon Iraqis forming an inclusive government, which they have now done in recent days," Obama said in his September 10 address announcing the new counter-ISIS campaign.

But the reality of the Iraqi government, thus far, suggests the opposite. "The government is composed mostly of Shia Islamists who may not differ from Maliki on many key issues," Fanar Haddad, an expert on Iraq's Sunni-Shia divide at the National University of Singapore, told me in an email. "In fact, the track record shows that the new government is likely to be more hardline than Maliki on contentious issues."

Haddad points to the new coalition's "voting patterns and positions" on two core Sunni-Shia issues as proof. First, they've been skeptical of decentralization, which means granting more autonomy to Sunni and Kurdish regions. Second, they've held up efforts to rewrite Iraq's de-Baathification law, which excludes former members of Saddam's government from holding positions in government. In practice, de-Baathification has been used to exclude Sunnis from important positions in the army and other major Iraqi institutions.

Indeed, some of the hardline Shia parties in Abadi's coalition helped scuttle an early 2013 proposal from Maliki and Sunni lawmaker Saleh al-Mutlaq to reform de-Baathification laws. Many of these guys, in other words, are significantly more hardline than Maliki.

So while Abadi himself has promised to govern more inclusively, his coalition may make that extremely hard to do. And until that changes, Sunnis will continue to feel alienated — and will turn to ISIS.

3) 0

According to the Washington Post, the US has failed to destroy a single major Islamist terrorist organization since 9/11. That's right: after the so-called War on Terror began, the United States hasn't managed to annihilate a single significant militant group. And Obama wants to make ISIS, one of the strongest such groups we've ever seen, the very first.

Obviously, America's failure isn't for lack of trying. It's because destroying terrorist organizations is quite difficult. These organizations, ISIS included, often have some level of support from the local population, which makes it easy for them to hide among civilians and recruit new fighters. They frequently have bureaucratic, decentralized leadership structures that make the loss of even high-level leaders insignificant. ISIS may be an exception here, as self-proclaimed Caliph Abu Bakr al-Baghdadi is quite important to the group, but it's tricky to make the case that ISIS will fall apart without Baghdadi so long as he's still alive.

Moreover, ISIS has a history of resiliency. During the later stages of the Iraq war, a Sunni uprising (called the Awakening) and an improved US offensive demolished what was then al-Qaeda in Iraq, reducing its membership by about 95 percent. Yet despite these losses, AQI rebuilt itself, and eventually morphed into ISIS.

"We're not going to see an end to this in our lifetime"

Obama cited US campaigns against Islamist militants in Yemen and Somalia as success cases. But, as ThinkProgress' Hayes Brown pointed out, al-Qaeda in Yemen, called al-Qaeda in the Arabian Peninsula, has weathered the US bombing campaign. The National Counterterrorism Center believes that AQAP is the terrorist group "most likely to attempt transnational attacks against the United States." And al-Shabaab, the Somali militant group, is alive and kicking, though the US and local allies have killed some of its leaders and pushed it back from its territorial high-water mark.

The point, then, is that everything we know about similar organizations suggests that the campaign against ISIS will take a long time, if it ever succeeds. ISIS can be weakened and pushed back, but destroying it outright is next-to-impossible.

"We're not going to see an end to this in our lifetime," Charles F. Wald, a retired Air Force general who oversaw the start of the air war in Afghanistan in 2001, told the Post.

It's not exactly a heartening thought.