Angela Merkel – or “leader of the free world” as she is now to be known – did not wait long to see the back of Donald Trump before she made it clear that things have changed. She told a rally of 2,500 people in Munich where she kicked off her campaign to be re-elected that the EU must now be prepared to look after itself, that it could no longer depend on the UK or America. “The times in which we could completely depend on others are, to a certain extent, over … I’ve experienced that in the last few days. We Europeans have to take fate into our own hands.”

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This is a truly dramatic statement from a leader who doesn’t do drama. She is not going to be holding Trump’s hand any time soon. He may be relieved to hear that, but then the underestimation of Merkel as a dowdy physicist has often allowed her to run rings around egotistical male leaders.

It was said to be a coincidence that she met Barack Obama the same day as Trump. It took a while for her to establish a friendship with Obama. She apparently disliked the “atmospherics” around him when he was first elected and wanted a more “conversational” relationship. She got it.

Watching her at the G7, her statesmanship, her ease, her ability to broker deals and relationships is ever more impressive. More and more I hear people say they that they like her. Even those on the left respect her though she is a centrist. While Trump shambled around Europe with his goon display of ignorance of other languages, cultures or even basic manners, Merkel was in her element. While he was trailing behind in a golf cart as he lacked the stamina to actually walk anywhere at all, she strode out with the other leaders.

Every gif of Trump shows him vacantly bumbling away, arrogantly shoving or being batted away by Melania. Gifs of Merkel, on the other hand, are a delight: her bemused expression when she has to deal with him, that twinkle, that little shrug she gives. She is at the top of her game – a game he has no idea how to play.

Merkel is at the top of her game – a game Donald Trump has no idea how to play

Vladimir Putin knew she was afraid of dogs, so brought a labrador to meet her on 2007. She didn’t flinch, later observing: “I understand why he has to do this – to prove he’s a man … He’s afraid of his own weakness.” No wonder Emmanuel Macron pulled off that wonderful swerve last week walking straight to Trump but greeting Merkel first.

Of course not everyone likes her. The Irish, the Portuguese, the Greeks, the Spanish and the Italians have felt the force of her pushing through stark austerity measures as the price of EU membership. At one point Greek protesters portrayed her with a Hitler moustache. Her expansionary politics, whereby every other country should seek to be as wealthy as Germany, have come at a huge price to countries she sees as fiscally irresponsible. Critics in Germany say she achieved a kind of “paralysed consent”. They complain about the number of opinion polls she has commissioned and her methodical, scientific way of dealing with politics.

Yet this, in reality, is why Mutti is considered so good at crisis management. Theatrics don’t interest her but there is a vision, a morality, a core to her that meant she could push through a policy of taking in refugees that required real guts.

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Asked if she was a feminist while sitting next to Ivanka Trump, Ivanka immediately raised her hand to say she was, and Merkel, who has done so much for women, hesitated and then said: “If you think that I am one, go and vote on it.” Friends say that she always considered herself emancipated by her studies and growing up in East Germany, where it was normal for women to work. Her husband, professor of theoretical chemistry Joachim Sauer, needs no security. They lead an unshowy life. The pictures of Merkel nipping out for chips, ecstatic at the football, drinking beer, are not set up. It’s what she does, though she no longer smokes or bites her nails to the quick in the way she did when she was younger. This all added to the geekiness that helped her to rise up through the party.

And look where she is now, unlike our prime minister, able to oppose Trump directly and to say his America is not a friend of Europe.

What an extraordinary woman. There are no problems, she says, only “tasks” to be solved, as she sits rapidly texting in meetings. Refusing to see herself as a female leader, she prefers to think of herself as part of a class of political heavyweights. Increasingly she is in a class of her own and watching her, one thought comes to mind: this is what strong and stable actually looks like.