By starting sooner, Mr. Zuckerberg said his money should go further. “Any good we do will hopefully compound over time,” he wrote. “If we can help children get a better education now then they can grow up and help others too in the time we might have otherwise waited to get started.”

Mr. Gates and the billionaire investor Warren Buffett launched the Giving Pledge, which asks wealthy people to commit to donating at least half of their fortunes to philanthropic causes during their lifetimes or upon their death. They want their fellow billionaires to act with urgency. On their own website, the Gates’ describes themselves as “impatient optimists.”

In June, Jeff Bezos, the founder of Amazon.com who, with a net worth of $84 billion or so, briefly supplanted Bill Gates as the richest person in the world this year, asked the public for some advice. “I’m thinking I want much of my philanthropic activity to be helping people in the here and now — short term — at the intersection of urgent need and lasting impact,” Mr. Bezos wrote on Twitter. “If you have ideas, just reply to this tweet.”

More than 48,000 replies flooded in. Mr. Bezos has not announced what he will do with his many billions, but his request for proposals was a reminder that there are untold fortunes that remain uncommitted to philanthropic causes. Nearly 200 people with a combined worth approaching $1 trillion have signed the Giving Pledge. New billionaires are beginning to ramp up their giving. Laurene Powell Jobs, the widow of Apple co-founder Steve Jobs, recently founded the Emerson Collective, which is putting money toward issues including education and immigration.

And as more people commit their fortunes to philanthropy, there will be many more organizations like the Open Society Foundations, and they may be with us for a long time. “The sun never sets on George Soros’s philanthropic empire, and the money is never going to run out,” said Mr. Callahan. “His money could still be affecting public policy 300 years from now.”

It is the dawn of a new era of big philanthropy. As wealth is rapidly created and concentrated, new mega foundations are being born, each reflecting its founder’s priorities. And much as Mr. Soros, Mr. Gates, Mr. Zuckerberg and the others in their cohort have eclipsed the titans of the Gilded Age, they are likely to one day be overtaken by an even newer crop of immensely wealthy and impatient optimists.