Mark Zuckerberg thought his fellow Silicon Valley billionaire Elon Musk was behaving like an alarmist.

Mr. Musk, the entrepreneur behind SpaceX and the electric-car maker Tesla, had taken it upon himself to warn the world that artificial intelligence was “potentially more dangerous than nukes” in television interviews and on social media.

So, on Nov. 19, 2014, Mr. Zuckerberg, Facebook’s chief executive, invited Mr. Musk to dinner at his home in Palo Alto, Calif. Two top researchers from Facebook’s new artificial intelligence lab and two other Facebook executives joined them.

As they ate, the Facebook contingent tried to convince Mr. Musk that he was wrong. But he wasn’t budging. “I genuinely believe this is dangerous,” Mr. Musk told the table, according to one of the dinner’s attendees, Yann LeCun, the researcher who led Facebook’s A.I. lab.