LONDON — Like pretty much everybody, Danell Leyva thinks Kohei Uchimura is the greatest male gymnast who’s ever lived.

For now.

While the three-time world champion was solidifying his exalted status with the Olympic title Wednesday, all but wrapping up the gold midway through the meet, Leyva gave a glimpse of what the young American hopes could be the sport’s next great rivalry. Closing with perhaps the two most spectacular routines of the night, the 20-year-old rallied to land in third place.

It was only the second all-around medal for a U.S. man since 1984, and added yet another chapter to Leyva’s incredible story. He fled Cuba as a sickly toddler with his mother and older sister, making their way to Miami through Peru and Venezuela.

“I’m going to keep working to beat him,” Leyva said. “His gymnastics is just so beautiful. ... I’m not trying to copy his style. I have my own style. I need to perfect me more to beat him.”

Uchimura finished with 92.690 points, almost two in front of Leyva. Marcel Nguyen won the silver, giving Germany its first Olympic medal in the men’s all-around since 1936.

When Uchimura finished floor exercise, his final routine, he gave a slight bow to the crowd before breaking into a wide grin. He pumped his fist toward several fans waving Japanese flags as he trotted off the podium, then graciously accepted congratulations from his competitors.

“I have been a world champion three times, three years in a row,” Uchimura said. “But this is different. It’s once in four years, and the wait was there. I felt like the demon was chasing me this time.”

That demon had about as much luck as the rest of the world. Uchimura has been untouchable since winning the silver medal in Beijing, so stylishly sublime that Germany’s Philipp Boy, runner-up at the last two world championships, lamented he had been born in “the wrong age.”

“He’s in a different world,” German coach Andreas Hirsch said. “He wasn’t part of this competition.”