Some years ago, the Irish politician and writer Conor Cruise O'Brien proposed this taxonomy of intractable international conflicts. They could be divided, he said, into "problems," which have solutions, and "situations," which can only have outcomes.

Among the most unyielding of the latter he placed South Africa, Northern Ireland and the Israeli-Palestinian impasse. At the time, O'Brien's dichotomy seemed an expression of tragic wisdom. History, however, has a way of humbling even the wise. No one could have had the foresight to envision what the dealings between Nelson Mandela and F.W. de Klerk would accomplish, nor imagined how far previously hard men — like Gerry Adams, Martin McGuinness and David Trimble — might bend.

That leaves the Middle East, where — for all the distractions of the global economic crisis — President-elect Barack Obama and his secretary of State-designate, Hillary Rodham Clinton, have an opportunity to push for peace and to reaffirm the centrality of the special relationship between the United States and Israel.

Anyone who doubts that should give close attention to an extraordinary interview with outgoing Israeli Prime Minister Ehud Olmert, a thorough English translation of which appears for the first time in the New York Review of Books' Dec. 4 issue. (You can read the whole thing online at www.nybooks.com/articles.) The interview is a translation of an extended conversation Olmert had with Nahum Barnea and Shimon Shiffer, who are — respectively — columnist and senior political correspondent for Yedioth Ahronoth, Israel's largest daily newspaper.

When this writer first met Olmert years ago, he was one of the right-wing Likud party's rising stars. He was smart, articulate, charming — and unyielding when it came to accommodation with the Palestinians or other Arabs. He made his name by opposing Menachem Begin's peace agreement with Egypt because it meant giving back the Sinai.

A great deal has changed since then, including Olmert's mind. As he told Yedioth Ahronoth, "We must reach an agreement with the Palestinians, meaning a withdrawal from nearly all, if not all, of the (occupied) territories. Some percentage of these territories would remain in our hands, but we must give the Palestinians the same percentage (of territory elsewhere) — without this, there will be no peace."

Olmert even dismissed the settler movement he once encouraged: "Who seriously thinks that if we sit on another hilltop, on another 100 meters, this will make a difference for Israel's basic security?"

Olmert told the journalists that he believes Israel is "very close to reaching agreements" with both the Palestinians and Syrians. When asked whether an accord with Damascus was within reach, the prime minister replied: "Yes, also with the Syrians. What we need first and foremost is to make a decision. I'd like to know if there's a serious person in the state of Israel who believes that we can make peace with the Syrians without, in the end, giving up the Golan Heights."

Olmert even argued that Israel must be ready to make territorial concessions in Jerusalem, where he once was mayor and which the Israeli right has long declared to be indivisible. He said there would have to be "special arrangements made for the Temple Mount and the holy/historical sites," but he was unequivocal that the city would have to be divided.

"Whoever talks seriously about security in Jerusalem ... must be willing to relinquish parts of Jerusalem. ... This decision is difficult, awful, a decision that contradicts our natural instincts, our deepest yearnings, our collective memories and the prayers of the nation of Israel for the past 2,000 years. I was the first person who wanted to maintain Israeli control over the entire city. I confess. I'm not trying to retroactively justify what I've done for the past 35 years. For a significant portion of those years I wasn't ready to contemplate the depth of this reality."

A close associate of Olmert's recently told The New York Times that the outgoing prime minister "is part of a group of one-time rightists who now seek a negotiated two-state solution largely because (they recognize) a change in Palestinian attitudes." Obama and Clinton should seize the opportunity. The flexibility to achieve moral progress through change is one of the characteristics of liberal democracies like the United States and Israel.

The common values of liberal democracy are the real basis for the special relationship between our two nations, and nothing would affirm or honor them more than constructive American engagement in a renewed Middle East peace process.

Tim Rutten is a Los Angeles Times columnist.