Judge Weinstein is one of the more than 1.5 million Americans over the age of 75, who are still in the paid work force, according to the Bureau of Labor Statistics.

While the study does not list their specific jobs, many work at occupations in which skill and brainpower count more than brawn and endurance. Some are self-employed and aren’t subject to mandatory retirement rules. Others are stars in their fields — no one has ever suggested that Warren Buffett, 87, quit investing. And there are others, a growing cohort, who remain at their posts because of financial necessity.

“The crash of 2008, debt burdens, decreasing income replacement rates and the demise of employer pensions are a few of the trends” that have pushed the number of non-retirees to record levels, said Susan K. Weinstock, vice president for financial resilience at AARP.

Ms. Weinstock said she expected that this trend would continue into the next decade. The Bureau of Labor Statistics says the labor force participation rate for those 75 and older rose from 6.4 percent in 2006 to 8.4 percent in 2016 and is likely to reach 10.8 percent by 2026.

For Adolfo Calovini, 82, a New York City high school teacher, the need to earn income is part of his motivation.