But in 1965, it all seemed to end abruptly, when Fleisher's right hand was gripped by a mysterious affliction. Like a hero from a Greek tragedy, he was struck down in his prime.
"When the gods want to strike, they know where to strike," says Fleisher. "They struck me in my hand."
Fleisher uses only one half of what most pianists have to work with. And yet, he can still fill a room with an eruption of intricate notes. He's now 76. But he began playing the piano at 4, and took to it instinctively.
He was the second son of Isidor and Bertha Fleisher, Jewish immigrants from Eastern Europe who settled in San Francisco. His father's business was to make hats. His mother's business was to make her son a great concert pianist.
"That's the extraordinary synchronicity of my life," says Fleisher. "A mother's wish for her child actually coinciding with the gift of the child."
But in order for that gift to grow, 11-year-old Fleisher needed to study in New York. So the Fleisher family moved in 1939. "My dad gave up his business in San Francisco, moved to New York and re-established themselves," he says.
Did it bother him that his parents moved so their son could be a success? "Yeah. Disruption," says Fleisher. "That's a terrible burden for a kid to bear."
But Fleisher was ready to prove that his family's sacrifices would pay off. At 16, he walked onto music's most famous stage, Carnegie Hall, to perform with the New York Philharmonic symphony orchestra.
Does he remember what he played? "D minor Brahms, first Brahms piano concerto," says Fleisher. "With Pierre Monteux, guest conductor."
The Nov. 20, 1944, issue of Newsweek magazine had this to say about Fleisher: "As the youngster made his way through the extremely long and extremely ungrateful Brahms D minor piano concerto, every critic in the house immediately recognized that here was no ordinary, youthful debutante of average promise."
"It was wonderful," says Fleisher, who was 16 when he performed at Carnegie Hall. His mother was there with him as well. "I think she was terribly proud. Terribly."
Fleisher had fulfilled his mother's dreams. He then moved to Europe to explore on his own. It was the Cold War and even classical musicians were being enlisted. In 1952, with Soviets dominating international music competitions, Fleisher entered a major contest as a representative of the United States. He won.
Soon, offers from orchestras began pouring in. "Leon Fleisher was one of the darlings of all the great conductors," says Leonard Slatkin, the conductor of the National Symphony Orchestra in Washington, D.C. "With Leon, you're overwhelmed with the thought that goes into the playing, and this incredible sound that comes out of the instrument."
That sound was captured in a series of celebrated recordings Fleisher made with conductor George Szell and the Cleveland Orchestra.
In 1963, they were planning a tour, sponsored by the State Department, of the Soviet Union and Europe, but something wasn't right.
"I noticed this kind of sluggishness in my fifth and fourth finger of my right hand," says Fleisher. "So I figured, 'Well, I better get back to work, work harder,' which is the worst thing I could have done."
His intense practicing was causing further damage. His fingers were curling up, and he couldn't will them to uncurl. "I knew I couldn't play with my right hand," says Fleisher. "My life was virtually over."
No doctor could tell him what was wrong. He fell into a deep depression, his marriage broke up, and he retreated into a social and musical isolation. "Absolute despair," says Fleisher. What did he think his life was going to be? "I didn't really know," says Fleisher. "I had no idea how I would support my family. Teaching seemed to be the only answer."
So he threw himself into teaching at the Peabody Conservatory in Baltimore. And, he found a new love, teaching, that continues to this day. He also tried conducting, and found that he loved that as well.
And then something remarkable happened. He ventured into a dusty corner of the piano literature, where he found pieces written exclusively for the left hand.