During his travels through New York, President Hassan Rouhani of Iran answered hundreds of questions, and even took a historic call from President Obama as he left town.
But to the American diplomats and intelligence officials who will conduct negotiations with Iran, the one question that really matters remained in the air, unaddressed, as Mr. Rouhani flew home to the difficult politics of dealing with Iran's military and its mullahs.
At the heart of the "significant concerns" that Mr. Obama said the two countries would have to address is whether Iran's divided leadership is really willing to dismantle vast parts of the multibillion-dollar atomic infrastructure it has amassed over the past decade as just part of the price for ridding the country of the sanctions that have crippled daily life.
In both Washington and Tehran, the internal politics of getting to an accord may be as hard as the negotiations that begin in Geneva in two weeks. The Islamic Revolutionary Guards Corps and the thousands of scientists, engineers and workers it has spread out across Iran will almost certainly face what Gary Samore, Mr. Obama's former top nuclear adviser, recently termed "sticker shock" at the price of easing the crippling sanctions imposed on their country.
On the list is dismantling a multibillion-dollar heavy-water reactor nearing completion -- a potential source of plutonium -- and halting production at, and ultimately destroying, a deep underground site, called Fordo, designed to be immune from Israeli air attack and American cyberattack.
And as midterm elections near, members of Congress who have approved ever-increasing sanctions may hesitate at voting to end the chokehold on the Iranian economy, starting with the steps that have halved its oil revenue.
Timing will be everything. Without drastic reversals on sanctions, the Iranians will be unwilling to walk back their nuclear advances, and vice versa.
"Tell me," one of the senior officials traveling with Mr. Rouhani asked a journalist on Thursday evening, after the president had spoken for an hour and a half. "If we create the right atmosphere, will Obama be able to tell the Congress to lift sanctions?" He went on to note the day's headlines, saying Mr. Obama might not have the votes to keep his own government running.
Perhaps the phone call Mr. Obama made on Friday began to narrow this chasm of distrust, at least suspending the chants about the "great Satan" that ring out at key anniversaries in Tehran, and ending the hangover of President George W. Bush's decision, nearly 12 years ago, to label Iran as a charter member of the "axis of evil."
At the core of the case for wariness is a word Mr. Rouhani kept repeating: "transparency." He was suggesting that after years of dodging inspectors on many issues, and cooperating on others, he was now prepared to let outsiders see enough to convince themselves that Iran's intentions are peaceful.
But when Mr. Rouhani was Iran's nuclear negotiator a decade ago, the country had only 164 centrifuges, the machines that spin at supersonic speeds to enrich uranium. That was essentially a science experiment, more worrisome than dangerous. Today there are 18,000, enough to enable Iran, if it decided, to race for a bomb, perhaps quickly enough to avoid detection.
Additionally, Iran's first heavy-water reactor (a potential source of plutonium, another bomb fuel) is nearing completion in the desert. Israel has told American officials it cannot allow this to go into operation.
Crucial questions -- of not only which nuclear fuel production facilities Iran will be permitted to maintain, but also what limits will be imposed on their capabilities -- are at the heart of what will make the negotiation so difficult, American officials say and some Iranian officials acknowledge.
"People have been telling them transparency is not enough," said Robert Einhorn, formerly one of the State Department's top Iran nuclear strategists and now at the Brookings Institution.
It would not be enough "to see a robust program where there is lots of I.A.E.A. monitoring," he said, referring to the United Nations' nuclear watchdog, the International Atomic Energy Agency. "The monitoring can be terminated suddenly. And once you have a robust program, breakout is relatively quick."
The Obama administration has seen what can happen when inspectors are thrown out. North Korea appears to have just restarted a reactor that was disabled in the last days of the Bush administration. So the issue is not simply getting the Iranians to remove and destroy most of the 18,000 centrifuges; it is also about what kinds of centrifuges Iran would build in the future.
As Mr. Rouhani was on his Manhattan tour, Iran was pressing ahead with installing a new generation of machines, now being deployed after a huge investment, in the same plant that the United States and Israel attacked from 2007 to 2010 with the most sophisticated cyberweapon ever used by one state against another. The new machines are believed to be four or five times more efficient than the aging, rickety models that the United States attacked, meaning it would take less time to produce bomb-grade material, should Iran elect to do so.
The new heavy-water reactor at Arak, nearing completion, adds urgency to any negotiations. Israel has made it clear it will not tolerate the start-up of that plant, and it has destroyed two similar plants -- one in Iraq in 1981, another in Syria in 2007 -- before they were fueled. Attacking it after fueling, experts say, invites creating a disaster as radioactive fuel is released into the environment.
And then comes the hardest question: whether, as part of the deal, Iran will let international inspectors talk with the man the C.I.A. and the West are most worried about, Mohsen Fakhrizadeh. Considered by the West to be Iran's equivalent to J. Robert Oppenheimer, the head of the Manhattan Project, which developed America's nuclear weapons in the 1940s, Mr. Fakhrizadeh has been hidden away, partly to avoid Israeli assassins.
Inspectors have never gotten answers to questions about documents that they say came out of his labs -- and that the Iranians say are fabrications. For Mr. Obama, the question will be whether to look forward, hoping to stop the production of nuclear material, or to insist on a detailed excavation of Iran's nuclear past.
Delving into that past will be a critical decision -- and potentially a critical point of difference with Israel's prime minister, Benjamin Netanyahu.
The Israeli goal in the negotiations (of which Israel is deeply suspicious) is to make certain Iran's production capability is so degraded that there would be warning of more than a year or two if it tried to race for a bomb. That means not only dismantling current infrastructure and putting caps on production, but also breaking up what American, Israeli and European intelligence agencies believe is a vast Manhattan Project of Iran's own, buried in the university labs under Mr. Fakhrizadeh's control.
But while it is possible to monitor a country's known enrichment sites, weapons labs are hard to find, and the knowledge of how to build a bomb impossible to erase. That will always leave lingering suspicions. Richard N. Haass, the president of the Council on Foreign Relations, who met Mr. Rouhani twice during the week, said at the end of the second session: "As difficult as this will be to negotiate, the implementation will be even harder."
This article originally appeared in The New York Times.