In a joint phone interview with Mr. Altman, Microsoft’s chief executive, Satya Nadella, later compared A.G.I. to his company’s efforts to build a quantum computer, a machine that would be exponentially faster than today’s machines. “Whether it’s our pursuit of quantum computing or it’s a pursuit of A.G.I., I think you need these high-ambition North Stars,” he said.

Mr. Altman’s 100-employee company recently built a system that could beat the world’s best players at a video game called Dota 2. Just a few years ago, this kind of thing did not seem possible.

Dota 2 is a game in which each player must navigate a complex, three-dimensional environment along with several other players, coordinating a careful balance between attack and defense. In other words, it requires old-fashioned teamwork, and that is a difficult skill for machines to master.

OpenAI mastered Dota 2 thanks to a mathematical technique called reinforcement learning, which allows machines to learn tasks by extreme trial and error. By playing the game over and over again, automated pieces of software, called agents, learned which strategies are successful.

The agents learned those skills over the course of several months, racking up more than 45,000 years of game play. That required enormous amounts of raw computing power. OpenAI spent millions of dollars renting access to tens of thousands of computer chips inside cloud computing services run by companies like Google and Amazon.

Eventually, Mr. Altman and his colleagues believe, they can build A.G.I. in a similar way. If they can gather enough data to describe everything humans deal with on a daily basis — and if they have enough computing power to analyze all that data — they believe they can rebuild human intelligence.