“I think it’s possible, but we don’t know,” Mr. Steck said of the route. “That’s exactly the challenge, that’s exactly the interesting thing. Nobody has done that before.”
Maurizio Folini, a pilot with a local helicopter company who brought Mr. Steck’s body to Kathmandu, said that it had been windy on Sunday and that Mr. Steck had fallen more than 1,000 meters. Tenji Sherpa, Mr. Steck’s trekking partner, was at Everest Base Camp when the accident happened, because he had frostbite on his hand.
“This is a big loss to mountaineering worldwide,” Mr. Sherpa, 26, said in a telephone interview. “I am shocked by his death.”
Mr. Steck’s body was to be taken to the Tribhuvan University Teaching Hospital for an autopsy.
A practitioner of the “fast and light” technique, in which climbers minimize the amount of gear and support they take on, Mr. Steck began his professional climbing career at age 18. Relying on a streamlined approach and his own remarkable endurance, he set several Alpine records, including the fastest ascents of the north face of the Matterhorn and the Eiger, as well as the Grandes Jorasses. In 2015, he reached the summit of all 82 of the 4,000-plus-meter peaks in the Alps in 62 days, nearly breaking another record.
Steve House, an American alpinist who knew Mr. Steck for about 15 years, said on Sunday that his friend had become a giant in the sport thanks to his focus on self-improvement.
“In our sport, you don’t become the best at age 18 or 20,” Mr. House said. “You become the best in your 30s and 40s, because it takes that long to get good at all the components that go into it.”
Mr. Steck’s work ethic “made him capable of accomplishing things that were simply otherworldly to the rest of the climbing community,” Mr. House added. “What he did was nothing short of miraculous, not only the speed records, but what he did and how he did it in the Himalaya. People just couldn’t understand it.”
Mr. Steck, who was born in Emmental, Switzerland, was known for his determination to complete challenging climbs, despite evident risks. A 2012 profile in Outside Magazine recounts how, after pledging to his wife, Nicole, that he would not make any more solo ascents, Mr. Steck endeavored in 2011 to climb Shishapangma, in Tibet, with a partner, the climber Don Bowie. After Mr. Bowie found himself unable to continue, Mr. Steck raced up the rest of the way alone.
On Sunday, Mr. Bowie shared a picture of himself and Mr. Steck on Instagram, saying he was “totally gutted” and “beyond sadness” at the news.
Mr. Steck, who twice won the Piolet d’Or award, mountaineering’s highest accolade, attracted some controversy along with the acclaim. In 2014, after becoming the first person to complete a solo climb up Annapurna’s main south face, some people doubted his achievement because he could not offer independent proof that he reached the summit. He was also one of several European climbers who brawled with a group of Sherpas in 2013.
Mr. Steck had climbed Everest before, and he took its challenges seriously. In a report from his successful summit in 2012, he reflected on the dangers. But he also recalled his frustration at falling behind other climbers.
“Surely I couldn’t be more tired than the others,” he wrote. “From now on I had to fight. I convinced myself that reaching the summit was only a matter of determination. And I decided that I would reach the summit.”
Last Monday, Mr. Steck told his Facebook followers that preparations for what would be his last expedition were going well. And in his YouTube video posted before his climb, he described himself as “super ready, I mean I’m so psyched,” adding, “For me the project is already a success.”