Those earlier barons disappeared by the 1920s and, constrained by the Depression and by the greater government oversight and high income tax rates that followed, no one really took their place. Then, starting in the late 1970s, as the constraints receded, new tycoons gradually emerged, and now their concentrated wealth has made the early years of the 21st century truly another Gilded Age.

Only twice before over the last century has 5 percent of the national income gone to families in the upper one-one-hundredth of a percent of the income distribution — currently, the almost 15,000 families with incomes of $9.5 million or more a year, according to an analysis of tax returns by the economists Emmanuel Saez at the University of California, Berkeley and Thomas Piketty at the Paris School of Economics.

Such concentration at the very top occurred in 1915 and 1916, as the Gilded Age was ending, and again briefly in the late 1920s, before the stock market crash. Now it is back, and Mr. Weill is prominent among the new titans. His net worth exceeds $1 billion, not counting the $500 million he says he has already given away, in the open-handed style of Andrew Carnegie and the other great philanthropists of the earlier age.

At 74, just over a year into retirement as Citigroup chairman, Mr. Weill sees in Carnegie’s life aspects of his own. Andrew Carnegie, an impoverished Scottish immigrant, built a steel empire in Pittsburgh, taking risks that others shunned, just as the demand for steel was skyrocketing. He then gave away his fortune, reasoning that he was lucky to have been in the right spot at the right moment and he owed the community for his good luck — not in higher wages for his workers, but in philanthropic distribution of his wealth.

Mr. Weill’s beginnings were similarly inauspicious. A son of immigrants from Poland, raised in Brooklyn, a so-so college student, he landed on Wall Street in a low-level job in the 1950s. Harnessing entrepreneurial energy, deftness as a deal maker and an appetite for risk, with a rising stock market pulling him along, he built a financial empire that, in his view, successfully broke through the stultifying constraints that flowed from the New Deal. They were constraints not just on what business could or could not do, but on every high earner’s take-home pay.