Which leads to the $64 billion question: Will Rowhani's election open a window for serious negotiations on Iran's suspect nuclear program? And will it prevent the military strike that Israel and President Obama have threatened if Tehran moves forward with its program - a strike that could ignite another Mideast war that nobody wants?
Optimists note that Rowhani was Iran's chief nuclear negotiator from 2003 to 2005, when the Iranians appeared ready for substantial concessions - and when they froze their uranium enrichment program. Pessimists say Rowhani simply puts a better face on a nuclear policy controlled by Iran's hard-line supreme leader, Ayatollah Ali Khamenei.
I readily admit that skepticism is wise when considering negotiations with Tehran. Yet I find myself tilting ever so slightly, with some caveats, toward the optimists' side.
Why so? First, one can't discount the surprising nature of the election. While no reformer, Rowhani was the most moderate of the six candidates who were permitted to run; he was not expected to be the winner. But moderates and pragmatists, including women and young people, united behind him at the last minute, giving him a majority in the first round of balloting. And - this is key - Khamenei decided the hard-liners couldn't afford to fix the election, as they did for Ahmadinejad in 2009.
Having recognized the need to address the growing frustrations of a majority of the population, the supreme leader must now weigh whether he can afford to frustrate them further with foreign policies that alienate much of the outside world.
Second, Rowhani has unique connections that cut across political lines and could facilitate negotiations. Unlike the previous two Iranian presidents, he is close to Khamenei, who may be willing to cut him more slack in nuclear talks than he did Rowhani's predecessors. At the same time, says the Carnegie Endowment for International Peace's Karim Sadjadpour, the new president is a "pragmatic conservative" who puts economic concerns above revolutionary ideology. (He appears to share the merchant mentality of former President Ali Akbar Hashemi Rafsanjani, with whom he is also close.)
"It is good to have centrifuges running," Rowhani said during one of Iran's presidential debates, "provided people's lives and livelihoods are also running." Clearly the president-elect is concerned about the economic impact of international sanctions caused by Iran's nuclear program. Such practical concerns may encourage him to negotiate seriously.
Third, the absence of Ahmadinejad will improve the atmosphere for negotiations. His Holocaust denials and calls for Israel to be "wiped off the map" convinced many that Iran might actually use a nuclear weapon against Israel if it could make one. Ahmadinejad's apocalyptic mind-set raised the question of whether he believed a war with Israel was required to expedite the much-awaited return of the Shiite Muslim Mahdi, or savior. (I once had a chance to ask him this question, and, in an incredibly long-winded way, he said no.)
The election of a more rational, economic-minded Iranian leader makes it far harder to imagine the ayatollahs risking their wealth and lives for a suicidal attack on Israel. That does not mean Iran should be allowed to develop a weapon, which could set off a nuclear arms race in the region. But it does clear the air before any talks start.
Which brings me to my caveats. The president-elect has already said his government won't again suspend its "right" to uranium enrichment, although this is a basic demand of Western negotiators. "Iran has created facts on the ground, and it would be very hard, short of an invasion, to remove them," said Michael Adler, a nuclear expert at the Woodrow Wilson Center in Washington.
Will Iran agree to sufficient limits on its program and intensive enough inspections to persuade the West to permit some enrichment for limited purposes? And will Ayatollah Khamenei, who must approve any deal, be willing to forgo the anti-Americanism so central to his ideology? It's not at all clear.
Nor is it clear that Rowhani can engender the trust needed to produce a compromise. At his first news conference, he tried to calm the fears of Sunni Gulf Arabs that Iran wants to dominate the region. But Iran's aggressive role in Syria - where it is sending money, arms, and men - puts the lie to such entreaties, especially when Rowhani insists that the Syrian people should decide their own fate.
Perhaps the question of Syria could be added to the negotiating agenda, but not while Iran's actions there threaten to ignite sectarian war throughout the region. This contradiction between Rowhani's words and his country's deeds underlines the question marks about future negotiations and how much of a difference the incoming president can make.
Trudy Rubin can be reached at email@example.com.