The United States never elected an African-American man to be president, until it did. The country also never elected a reality television star to become president, until it did.

So as the nation’s mayors gather in Boston this weekend for the US Conference of Mayors — an event largely focused on the nuts and bolts of how to make their respective cities better — at least three in attendance are thinking about shattering another historical precedent: going directly from City Hall to the White House in 2020.

Unlikely as it may seem, the United States has never elected a mayor directly to the presidency. In fact, the last time a major party even nominated a sitting mayor to be president was in 1812, when New York Mayor DeWitt Clinton was nominated, only to lose to the incumbent, James Madison.

In the two centuries since, that record hasn’t improved: Only two of the country’s 44 presidents even held the title of mayor at any point before ascending to the presidency. That includes Calvin Coolidge, who served as mayor of Northhampton before assuming roles on Beacon Hill and later serving as vice president.

But none of that history has stopped three Democrats, Los Angeles Mayor Eric Garcetti, South Bend, Ind., Mayor Pete Buttigieg, and Mitch Landrieu, the recent former mayor of New Orleans, from having 2020 stars in their eyes.

All three men are in Boston this weekend for the conference. And all three have said they wonder if this is a unique time in America, where dysfunction in Washington — and increasingly at the state level — will have voters looking for fresh blood from pockets of this country where governments might actually be working. Cities like theirs, they argue, are a natural place to look.

After all, mayors, by definition, are the ones who must actually do something about problems such as rising housing costs, racial unrest between civilians and police, and struggling schools. As Garcetti noted in an interview with the Globe on Thursday, “Literally, it is our job to make sure the trains run on time.’’

Buttigieg told the Globe it’s not even worth fretting about the usual election playbook this time around.

“The president of the United States is a game show host, so if you are looking for historical precedents, it just doesn’t really fit the times,’’ he said. “Some people might get carried away and conclude that there are no rules anymore, which is probably not true, but we don’t know which rules still apply and which have been shattered.’’

With that in mind, all three have taken on robust travel schedules that have already brought them to early presidential primary states like Iowa and New Hampshire. Since leaving the job last month, Landrieu is out with a new book about his time as mayor (a sure sign of presidential aspirations). And as the outgoing chair of the US Conference of Mayors, he also gave a major speech Friday morning at the Copley Marriott that will be closely analyzed by political observers for any hints of future ambitions.

Garcetti notes that the mayoral crop as a whole is a group worth watching.

“I have been quite open about looking at the presidential race,’’ Garcetti said. “I think that there is a network of mayors innovating and have the trust of real Americans and I think we have something to add to the conversation.’’

Overall on the Democratic side, the 2020 field is bound to be an anomaly. The group could feature as many as 20 major candidates, from governors to US senators to business people and celebrities. In that environment, who is to say that a mayor who runs South Bend, the 301st-largest city in the country, can’t have a shot?

With the Clintons fully off the stage for the first time in two decades, observers are also saying the Democratic Party has finally recognized that it’s time for something entirely new. That may involve pushing a candidate who has never served a day in Washington.

Garcetti and Buttigieg are counting on that perspective, and touting what makes them each a fresh face. Garcetti jokes he is one-eighth of everything, including the fact he is the city’s first Jewish mayor and second-ever Mexican-American mayor, despite his Italian last name. Buttigieg, meanwhile, spends a fair bit of energy discussing his experience being deployed to Afghanistan for seven months and speaking candidly about his experience as a gay man now engaged to be married.

For Landrieu, the argument has more to do with the nuts and bolts of what he accomplished thousands of miles from Washington — pushing to remove a number of Confederate monuments and leading a city still working to recover from Hurricane Katrina, even 13 years on.

Democratic strategist James Carville, who lives in New Orleans, has told Politico that he believes Landrieu is in the same league as Bill Clinton and Barack Obama when it comes to raw political talent.

So what does that mean for this weekend’s conference? With the gathering now underway in the Back Bay, Landrieu, Garcetti, and Buttigieg can surely be expected to use their time here to make the case for their potential candidacies. It’s a big leap from city hall to the Oval Office, but these are strange times and Massachusetts has seen stranger political ascents.

James Pindell can be reached at James.Pindell@globe.com