Retired neurosurgeon Ben Carson and former tech executive Carly Fiorina — two novice politicians whose attacks on Democrats have made them conservative stars — both declared Monday that they are running for president as Republicans.

Carson, 63, held a highly stage-managed event in his hometown of Detroit: The candidate took the stage after several musical numbers, including “The Battle Hymn of the Republic” and Eminem’s “Lose Yourself.”

“I’m Ben Carson, and I’m a candidate for president for the United States,” Carson said, before declaring that “I’m not a politician.” Carson will now visit his gravely ill mother in Texas, before flying to Iowa.

Fiorina, 60, made her announcement in a web video, and an appearance on ABC’s “Good Morning America.” After losing a Senate race in California in 2010, Fiorina has relaunched her political career by lobbing attacks at Democratic front-runner Hillary Rodham Clinton. On ­Monday, her video began with ­Fiorina watching Clinton’s own announcement, then raising the remote and turning off the TV.

“If you believe that it’s time for citizens to stand up to the political class and say, ‘Enough,’ then join us,” Fiorina said. “We can do this, together.”

Both Carson and Fiorina led remarkable, pathbreaking lives before politics. But, in their short time on the national political stage, they have both been defined — and limited — by the same set of skills.

They are masters of the attack line.

Carson, a pioneering black surgeon, began his political rise by attacking President Obama’s health care law — with Obama sitting nearby — at a prayer breakfast in 2013. Fiorina, a pioneering female executive, has relentlessly criticized the most prominent woman in the race.

Because of who they are, Carson and Fiorina can articulate conservative frustrations with Obama and Clinton, while blunting a potent line of Democratic counterattack — if you dig deep enough, some criticism of Obama and Clinton has its roots in racism or sexism.

If the pair want to do more than disrupt the race, they will have to expand far beyond the role of punch-thrower. And they will need to avoid the problems that usually sink nonprofessional politicians running for president: verbal gaffes and poor preparation.

Not to mention the tendency to think through ­sensitive ­subjects out loud, on camera. “I don’t wander off into those extraneous areas that can be exploited. I have learned that,” Carson said in a TV interview on Sunday evening.

Carson and Fiorina officially join a trio of senators — Ted Cruz of Texas, Rand Paul of Kentucky and Marco Rubio of Florida — in the GOP field. In many polls, the newcomers are behind all three of them. They’re also behind two ­candidates who aren’t even officially candidates yet: former Florida Gov. Jeb Bush and Wisconsin Gov. Scott Walker.

For now, Carson seems like the less long of the two long shots. In March, a Washington Post-ABC News poll showed him with the support of 6 percent of GOP voters. With the electorate divided among a number of candidates, that’s not bad, actually. It puts him in the middle of the pack: In South Carolina and Iowa, that kind of number puts Carson in the top six.

On Monday, Carson returned to his personal story. In a video that played before he spoke, his message seemed to be that, if he became president, he could imbue the country with the qualities that underlie his own personal success.

“Healing requires a leader with calm, unwavering resolve,” the video said. “We have the fortitude to heal, the imagination to inspire and the determination to revive our American dream.”

For Fiorina, the first challenge will be to raise her poll numbers. She gets only about 1 percent support among Republicans nationally.

The good news is that a lot of people don’t know Fiorina yet: And in a recent swing through Iowa, she attracted unexpectedly large crowds, more than 100 at some events.

“We have time,” Fiorina said with a laugh during a conference call on Monday. “There has been greater reception to my candidacy than I think many might have expected.”