Eliminating the world’s top 20 diseases, such as AIDS, malaria, and tuberculosis, is achievable, William Gates III said yesterday after he and his wife, Melinda, accepted a $31 billion gift to their Bill & Melinda Gates Foundation from Berkshire Hathway’s chief executive, Warren Buffett.

The gift, presented at the New York Public Library, along with gifts to his children’s foundations and to the foundation named after his late wife, doubles the size of the Gates foundation, whose grant-making is likely to increase to $8.2 million a day from $4.1 million.

Mr. Gates has an even larger goal. “When you improve health, you reduce population,” he said.”Then you get into a cycle of building infrastructure and government stability and you’re on track to eliminating global inequity.”

That’s the kind of bold thinking the foundation is known for, and which attracted Mr. Buffett to its work. He admired the Gates’ approach of giving to high-risk projects that other entities refused to support, but he prefers to let them pursue that approach without his interference, he said. He will become a trustee of the foundation.

“This has all the markings of a home run to be able to tackle some serious challenges,” the president of the New York Regional Association of Grantmakers, Michael Seltzer, said. “They’re starting with a strong track record that will enable to bring successful initiatives to scale.”

The Gates gave only a preliminary outline of how the foundation would respond to the gift, which comes in the form of annual allocations of Berkshire Hathaway stock. They have two years to ramp up before they’re obliged to start spending Mr. Buffett’s money.

“We’re going to deepen and accelerate our commitment in areas we’re already into, not broaden, particularly in education and global health,” Mrs. Gates said. She added that the staff of 300 would grow, but emphasized that the foundation’s model is to be a “convener, building partnerships.”

“They will need more oversight, and they’re going to need stronger partners, so I’d guess they’d have to invest more in capacity building among their grantees,” a professor of nonprofit management at New York University, Paul White, said. “They’ll need to do due diligence more aggressively given the size of grants they make,” he said.

The Gates would like their example to inspire others, whether it’s giving close to home or across the globe. However, the Gates Foundation isn’t accepting gifts at the moment. That could change, Mr. Gates said, “if there’s a lot of interest.”

“This act sends a very strong signal to their peers in the ultra-high net worth categories that it’s important to think about ways to collaborate and not to compete,” the senior vice president at Rockefeller Philanthropy Advisors, Douglas Bauer, said.

To show their appreciation for Mr. Buffett’s gift, the Gates presented him with two books by Adam Smith from their personal library, “The Theory of Moral Sentiments” and “The Wealth of Nations.” They’ve also started giving him homework: a 192-page book about disease.