In recent days, it has seemed as if President Donald Trump was ready to challenge Secretary of State Rex Tillerson to an IQ contest. Perhaps Trump should extend the same challenge to the EU's top diplomat, Federica Mogherini. Who would win?

"That's easy," said Middle East expert Koert Debeuf, with a smile on his face. But such a victory wouldn't be much comfort for Mogherini if the US ends up abandoning the 2015 nuclear agreement with Iran. Trump would essentially be killing the art of diplomacy in favor of nuclear saber-rattling. Thus, the great expertise Europe has shown in negotiating compromises would be of no use to anyone.

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To put it in the words of an EU diplomat who didn't want to be named: "The message would be: 'Do not negotiate! Especially not with the West, which doesn't keep its promises anyway.'"

The West no longer exists

Europeans want to save the deal, no matter what the US does.

"The nuclear deal doesn't belong to one country, it belongs to the international community," said Mogherini after a highly unpleasant conversation with US representatives on the sidelines of the UN General Assembly in New York last month.

If Trump's government withdraws from the deal and imposes new sanctions on Iran while Europe preserves the agreement, then an important aspect of the post-war world order would be lost: the unity of the West. Debeuf, director of the Brussels office of the Tahrir Institute for Middle East Policy, believes the EU should by no means give in to the US, as it has until now.

"Europe should invest more in Iran. This is important for Europe's credibility and the reform forces in Iran," he told DW. Of course, pressure from Trump can be expected, probably in the form of US sanctions against European companies doing business in Iran.

A stronger, weaker Europe

Here's something to think about: If the US withdraws from one of the greatest diplomatic successes of the past decades — a nuclear disarmament agreement that works — no one is likely to take the nation seriously any longer. Europeans, on the other hand, would end up being the only ones able to guarantee stability, integrity and credibility, and would surely be applauded for this around the world.

But harsh reality would eventually catch up. "Behind closed doors in Iran, no one believes that the Europeans can make a difference without US involvement," said Jamsheed Faroughi, head of DW's Farsi department. 

Without the US and its military muscle, the value of Europe's negotiating skills would drop considerably. The US and Europe work in tandem with each other. Europeans could gain more respect, but they would probably lose their influence.

Read more: Iran deal: Trump has Europe concerned

Mogherini's greatest achievement at risk

At a press conference after the meeting on Iran during the UN General Assembly, Mogherini's gestures revealed her underlying anger. Her team, however, chose to call it "determination."

The EU's highest-ranking diplomat is by no means the only one responsible for the 12 years of negotiations that led to the successful Iran deal, but she is nonetheless very proud of it. If her reputation is damaged, then the EU may no longer be perceived as a unified entity on the international stage.

"To put it quite simply, Europeans are currently the good guys and Americans are the bad guys," said Faroughi, referring to the prevailing image of Europe in Iran.

However, if EU diplomacy fails, individual member states could rise to prominence once again.

No good neighbors

Flanked by Vladimir Putin's Russia to the east, the Syrian conflict to the southeast and Libya to the south across the Mediterranean Sea, Europe has not been blessed with particularly pleasant neighbors in recent times. If Iran no longer feels obligated to abide by the nuclear agreement because the US is walking away from it, then the situation will become even more unpleasant.

As a consequence, the Iran deal would suddenly no longer be the blueprint for possible negotiations with North Korea. "What North Korea does is also a model for the Iranian government," said Faroughi. In other words, nuclear disarmament would be replaced by rearmament and thus, be followed by further destabilization in the entire region. And not just Europe would be affected.

"This is about world peace," said Debeuf, with a sigh. "We must take Iran very seriously and communicate with Tehran." A message that doesn't appear to have reached the US president.