Ronald Reagan and Mikhail Gorbachev met at Reykjavik on October 11 and 12, 1986, in a meeting that was meant to clear the way for a later summit and instead became the nearest the two powers ever came to doing away with nuclear weapons. It ended in failure, and is remembered for how close it got to succeeding, which is not the usual shape of a failed negotiation.
It was arranged in haste. The leaders had met at Geneva the year before and agreed that a nuclear war could not be won and must never be fought, but nothing had been agreed on numbers, and Reykjavik was to be a working session to prepare the Washington summit. The delegations brought far more than expected, and over the two days the offers ran ahead of anything their own staffs had cleared. Gorbachev proposed cutting strategic warheads by half. Reagan answered, and the two men found they were discussing the abolition of all ballistic missiles, then of all nuclear weapons, with the numbers being written on the table in front of them.
It fell apart over one thing: the Strategic Defense Initiative, Reagan's shield in space. Gorbachev made the whole package conditional on confining SDI to the laboratory, and Reagan would not give up what he insisted was a defence and the Soviet side insisted was the first stage of an arms race in space. They left without a document.
The pieces were picked up the following year. Out of Reykjavik came the Intermediate-Range Nuclear Forces treaty of 1987, the first agreement to eliminate an entire class of weapons, with inspections on the ground in both countries, and the framework for the cuts in strategic arms that followed. Reagan's shield never came. What did come out of the two days was the shape of the end of the Cold War, worked out in a house outside Reykjavik and written down on a tabletop.