His outrageous actions, statements and attitudes are upsetting constitutional, political, diplomatic and economic norms — not least his audacious proposal that the US take over Gaza and oversee responsibility for redeveloping it as "the Riviera of the Middle East".
It is tempting to reject everything Mr Trump says as nonsense and lies, or at the very least distorted exaggerations.
He is, after all, an unenlightened narcissist with an elephantine ego.
But he is cunning, he "thinks outside the box", he cuts to the chase as he sees it, and he is continually underestimated.
Most people think the Gaza idea is plain bonkers for a bombardment of reasons.
Many of the Palestinians would refuse to leave, Egypt and Jordan have said they would refuse to take them, the US would somehow take charge without spending money and without "boots on the ground", US action would blatantly violate international law, Hamas is not going away, and so forth.
Has not the United States learned the lessons from Vietnam, Iraq and Afghanistan of the perils of foreign entanglements?
There is, of course, no detail on the idea to critique.
Meanwhile, Mr Trump sanctions the International Criminal Court, stops aid to South Africa and provokes allies with threats.
His sidekick, Elon Musk, the unelected Department of Government Efficiency (Doge) Tsar, scythes into government with bewildering and dangerous power and purpose.
Shutting down almost all the United States Agency for International Development is brutal, cruel and unwise.
USAID is, according to Mr Musk, "a viper’s nest of radical left Marxists who hate America". But US aid, for all its weaknesses, provides vital support and relief around the globe. It is, crucially, a key pillar of US "soft power".
Israeli President Benjamin Netanyahu seemed to have been caught on the hop by the Gaza plan, just like many of Mr Trump’s senior officials. Mr Netanyahu was, however, delighted.
It has also been suggested that Mr Trump — who yearns to be remembered as a "peacemaker" and a visionary — is just being himself. As he said in his book The Art of the Deal, "a little hyperbole never hurts" and "I play to people’s fantasies".
Does the outrageous and unthinkable earn support from Mr Netanyahu and the hard right in Israel and, down the line, allow them to agree to a modest compromise?
Who would know with Mr Trump?
Is he, as supporters would have it, the king of negotiation and the prince of brinkmanship? Does he bring fresh ideas and a "muscular" approach that gets results?
South and Central America — and especially Panama — has certainly received the message that they should back off from their enthusiasm for China and its Belt and Road infrastructure initiatives.
But the complexities of the world order, the relative peace since World War 2 and the rights and balances between nations are subtle and shaky.
Mr Trump will increasingly find that the relative simplicity of a hotel or golf resort deal is nothing compared with the depth and delicacy of diplomacy.
His style of winning while the other party loses negates the gains possible when negotiations can benefit both sides.
Mr Trump’s claim of ending the war in Ukraine as soon as he took power has, naturally, not eventuated. Nonetheless, he will be turning his rapid-fire attention in that direction soon.
That, too, will be a phenomenal test of negotiation ability. Just selling out on Ukraine will be a failure and a sad indictment of a new world order where country borders are no longer inviolate and protected by international law and precedent.
While Mr Trump has talked tough about Russian President Vladimir Putin, he has proved his hyperbole, and his fantasies cannot be trusted.
Likewise, his gazing into an imaginary future for Gaza is likely to prove to be nothing but blustering baloney.
