ATHENS — For all the chest-thumping and heated rhetoric between President Obama and President Vladimir Putin of Russia in recent weeks, efforts by the West to make Moscow’s maverick leader pay for pushing his forces through Crimea have failed — miserably. U.S. and European officials already acknowledge that Crimea is a lost cause, and some assert that Putin’s lightning takeover and annexation of the peninsula mark the start of a new Cold War.

The challenge now, experts explain, is stopping Russia’s capricious autocrat of 14 years from further destabilizing Ukraine. That means stiffer sanctions if Putin provokes further trouble. But if he doesn’t, preferring instead to just pocket his victory in Crimea and leave it at that, then the way could be paved for negotiations that would allow for Ukraine’s besieged and harassed military personnel to exit Crimea peacefully, followed by free elections in Ukraine to install a legitimate national government, revamp the economy and create durable institutions.

Whatever the solution, if any, it most probably depends on German Chancellor Angela Merkel and the tetchy ties that the de facto boss of the European Union has with the Russian president.

Ever since Putin drove a tank through world order, in effect, by annexing Crimea, Merkel has made but a handful of cautiously worded public remarks, mainly underscoring the need for preserving the territorial integrity of Ukraine. But behind the scenes, the world’s most powerful female leader is at the center of it all. U.S and European officials acknowledge that if anyone can exercise any influence on Putin, potentially getting him to pull his troops back to their bases, she can.

In the 14 years they have known each other, Putin and Merkel have grown to understand each other’s realities better than most. Both built their political careers against the backdrop of tumultuous events in Eastern Europe in the final years of the Cold War. While Merkel won a prize trip from East Germany to Moscow, to learn Russian, in 1969, Putin acquired some of his fondest memories — and fluent German — in Dresden, where the KGB stationed him as a Soviet spy in the 1980s.

Both watched the fall of the Berlin Wall from the same side, but each, ironically, drew different lessons. A physicist and daughter of an East German pastor, Merkel came to praise the United States as a world beacon of freedom. Putin, by contrast, fed on designs of revanchism as he eventually watched the Soviet empire crumble.

She rose through the ranks of German politics, breaking through gender quotas as a cautious strategist while gaining enormous popularity and solid approval ratings. He came to fancy thuggish shows of strongman rule, purportedly harassing diplomats and intimidating foreign leaders, while domestic critics and opponents were jailed, threatened or assassinated.

On one occasion, Putin attempted to frighten Merkel during talks at his summer home years ago, letting his black labrador, Connie, run loose around the German leader, who is known to fear dogs since being bitten by one in the 1990s.

Today, Merkel finds herself mediating at times between Obama and Putin. And while she is said to have recently informed the U.S president that his Russian counterpart had seemingly lost touch with reality and was “in another world,” according to the New York Times, she is the only foreign leader to hold Putin’s ear.

“Both leaders respect each other’s toughness,” says Dimitris Skiadas, a professor of European Studies in Greece. “But with Germany reliant on Russia for over a third of its energy needs, it’s no wonder she has been on the phone to him almost daily.”

By exporting large quantities of precision machinery, chemicals and luxury cars to Russia, Germany, Europe’s powerhouse economy, has an economic relationship with Moscow that gives Merkel some leverage against Putin.

“Although other European leaders have come out stronger and harsher against Putin,” Merkel has worked to moderate Europe’s response, Skiadas says. “This speaks volumes about the geopolitical interests Germany is trying to preserve, not gender politics.”

Perhaps. But it does say something about female leadership.

Although frequently compared to that of the late British prime minister Margaret Thatcher, Merkel’s leadership style could not be more different. “Thatcher ruled with an iron fist [and] loved to be called the Iron Lady, toting her purse and betting on her role as a woman,” Skiadas says.

Merkel hasn’t.

While dealing with prejudice throughout her career, the German leader, who grew up in East Germany, has been reluctant to emphasize her femininity. She rarely talks about feminism, flaunting instead the austerity-driven Frauenpolitik that she subscribes to, preferring debate, deliberation and consensus. What’s more, despite the many names she has been called — including “bulldog” and “minx” — Merkel has aligned herself more with the nickname “mutti,” an affectionate German word for mother. It denotes a trademark type of leadership that many women, regardless of political affiliation, claim they can relate to. In the latest election last September, Merkel secured 44 percent of the women’s vote.

She does not, of course, lack critics, who have called her a “monster” for arm-twisting European Union leaders to adopt austerity measures as an antidote to Europe’s lingering debt crisis.

Whether Merkel’s mediation attempts will amount to anything in the ongoing Crimea crisis remains uncertain. But with the West facing the prospect of drifting back into a Cold War era with Russia, the German leader represents the best chance of preventing such an outcome. Polls show that just 3 percent of Russians respect Obama, compared to 20 percent for Merkel, making the world’s most powerful woman the West’s most credible communicator with Russia.