When federal prosecutors announced sex-trafficking charges against Jeffrey Epstein this week, they described him as “a man of nearly infinite means.” They argued that his vast wealth — and his two private jets — made him a flight risk.

Mr. Epstein is routinely described as a billionaire and brilliant financier, and he rubbed elbows with the powerful, including former and future presidents. Even after his 2008 guilty plea in a prostitution case in Florida, he promoted himself as a financial wizard who used arcane mathematical models, and he often dropped the names of Nobel Prize-winning friends. He told potential clients that they had to invest a minimum of $1 billion. At his peak in the early 2000s, a magazine profile said he employed 150 people, some working out of the historic Villard Houses on Madison Avenue.

Much of that appears to be an illusion, and there is little evidence that Mr. Epstein is a billionaire.

Mr. Epstein’s wealth may have depended less on his math acumen than his connections to two men — Steven J. Hoffenberg, a onetime owner of The New York Post and a notorious fraudster later convicted of running a $460 million Ponzi scheme, and Leslie H. Wexner, the billionaire founder of retail chains including The Limited and the chief executive of the company that owns Victoria’s Secret.