Charles Ponzi did not invent the Ponzi scheme. He just ran it so loudly that his name stuck.
He was born Carlo Pietro Giovanni Guglielmo Tebaldo Ponzi on 3 March 1882, in Lugo, Italy. He arrived in Boston on 15 November 1903 with $2.50 in his pocket, according to Wikipedia.
His big idea involved international reply coupons. These were vouchers a letter writer could buy in one country and send abroad, where they could be swapped for postage. Postage rates differed between countries, so in theory a coupon bought cheaply in Europe could be redeemed for more in America.
In January 1920 Ponzi opened the Securities Exchange Company. He promised a 50 percent profit in 45 days, or 100 percent in 90. The coupon trade could never work at that scale. History.com says that when it failed, he paid earlier investors with money from new ones. By June 1920, Wikipedia says, investors had put in $2.5 million.
The Boston Post began publishing articles on 26 July 1920 that questioned how the scheme could work. In August 1920 Ponzi surrendered to federal authorities on mail fraud charges. He went to prison, was deported to Italy in 1934, and died in a charity ward in Rio de Janeiro in 1949.
The con was old long before Ponzi. Wikipedia says Charles Dickens described such a scheme in Martin Chuzzlewit (1844) and Little Dorrit (1857). In the 1880s Sarah Howe ran the "Ladies' Deposit," promising women 8 percent a month. In 1899 a Brooklyn bookkeeper, William Miller, known as "520% Miller," took in about $1 million the same way. Wikipedia says Ponzi may have been inspired by him.
So why Ponzi's name and not theirs? Wikipedia points to scale and publicity. His scheme drew heavy press coverage in the United States and abroad. History.com puts the losses at about $10 million.
Dictionaries disagree on when the phrase appeared. Merriam-Webster dates "Ponzi scheme" to 1920, the year of the scandal. Etymonline gives 1957. Either way, the name now covers any fraud in which early investors are paid with later investors' money.
Wikipedia draws one useful line. In a Ponzi scheme, the fraudster deals with every victim directly. In a pyramid scheme, the recruits profit by bringing in more recruits.