The spotlight rarely found Ben Carson this summer. While other presidential candidates shot flaming arrows at rivals and sometimes the news media, the soft-spoken Mr. Carson seemed to struggle to be noticed. “Well, thank you,” he told moderators in the first Republican debate. “I wasn’t sure if I would get to speak again.”

But while almost all Republicans were upstaged by the bombast of Donald J. Trump in recent months, Mr. Carson, a retired neurosurgeon whose low-key personality and celebrated medical career are the antithesis of a politician’s usual path, gained ground as few seemed to notice.

A recent Quinnipiac University national poll showed him in second place in the Republican field, and a Monmouth University survey of Iowa Republicans released on Monday had him tied with Mr. Trump. Another Iowa poll, by The Des Moines Register and Bloomberg, had the two candidates running closely within the poll’s margin of sampling error.

Like Mr. Trump, Mr. Carson has never held elected office, a quality that seems particularly prized by Republican voters this year. More than 90 percent of voters in the Register/Bloomberg poll, conducted last week, said they were unsatisfied or “mad as hell” with government and politicians.