Critics have often been bamboozled by the former reality TV star's far-fetched proposals -- wondering whether he is for real, marking a negotiating position, or simply creating a distraction.
But Trump also prides himself on being a political disruptor -- and his shock suggestion to move out Palestinians and make Gaza the "Riviera of the Middle East" is a prime example.
"Much of what President Trump says is hyperbole, clever negotiating, and serious all at the same time," Peter Loge, the director of George Washington University's School of Media, told AFP.
"When he says outrageous seeming things that don't happen he plays it off as a joke or negotiating tactic. When the occasional scheme pans out, he claims to be a genius."
Trump's favorite tactic is often to leave people guessing.
A famous early assessment of Trump in 2016 by the journalist Salena Zito got to the heart of the difficulty.
Zito said that the press took Trump "literally, but not seriously" while his supporters took him "seriously, but not literally."
And offbeat suggestions have become 78-year-old Trump's trademark.
On one infamous occasion in 2020, he mused about injecting disinfectant to treat Covid-19 infection, or somehow getting a form of sterilizing light inside people's bodies.
In another case, before taking office in January, he vowed to end the Ukraine war in 24 hours.
And more recently, he stunned the world by suddenly talking about annexing Canada and Greenland and seizing the Panama Canal.
- 'Outside of the box' -
Trump's opponents have sometimes lived to regret not taking him seriously.
Many counted Trump out after his attempts to overturn his 2020 election loss, only to see him return.
Then they wondered if he would carry out the radical right-wing agenda he promised in his 2024 election campaign, just to see him launch a "shock and awe" program targeting immigrants, transgender people and the federal government.
But many of those measures now face challenges in the courts or in Congress, where his party has only the slimmest of margins.
The Gaza proposal, meanwhile, goes a step further in terms of sheer unpredictability.
A smiling Israeli Prime Minister Benjamin Netanyahu praised Trump Tuesday for "thinking outside of the box."
"You say things others refuse to say. And after the jaws drop, people scratch their heads and they say, 'you know, he's right,'" Netanyahu said.
But Middle Eastern leaders begged to differ.
And without any further elaboration from Trump, the White House and State Department have since had to walk back elements about whether it would be a permanent change and if it would involve US boots on the ground.
- 'Art of the Deal' -
Experts suggest there are different strategies for Trump's outrageous suggestions.
Sometimes they are useful as a distraction from more pressing political problems.
Mirette Mabrouk, senior fellow at the Middle East Institute in Washington, said Trump's recent proposals masked the fact that he had yet to bring down inflation as he'd promised.
"There have been these big international claims, but really none of this contributes to the price of eggs," Mabrouk said.
At other times, the man behind the 1987 book "The Art of the Deal" appears to use them as a negotiating tool.
This tactic seemed to be on display when Trump threatened tariffs on allies Mexico and Canada, then paused them after they agreed to take border security steps.
But things were, again, not necessarily as it seemed, as some of the Canadian promises had already been announced months earlier.
Trump's former career as a real estate tycoon -- albeit one that involved a series of bankruptcies and lawsuits -- perhaps provides the best explanation.
His plans for Gaza, Greenland and Panama all sound a lot like property deals.
Last year, Trump described Gaza as being "like Monaco," while his son-in-law Jared Kushner suggested that Israel could clear Gaza of civilians to unlock "waterfront property."
It was during Trump's property developer life in the 1980s, meanwhile, that he first floated a presidential run.
Few took him seriously at the time. Decades later, he would end up in the White House -- twice.
© Agence France-Presse
