She was a sickly child. At 9, she contracted scarlet fever. “After that, the doctor said, ‘You know what?’” she recalled. “‘We’ve tried everything. Let her dance.’”

She was short, her turnout was nonexistent and her feet needed a lot of work. She is firm about one thing: If her young self were to audition for the School of American Ballet today, she wouldn’t get in — much less into the company. It was never easy for her, but dancing meant too much to quit, even when her teacher took her, at 12, to see Mia Slavenska, a star of Ballet Russe de Monte Carlo, perform at Radio City Music Hall. Afterward, they met Slavenska backstage.

She asked for some pliés. “I did two pliés, and she said, ‘Forget it,’” Walczak said. “‘She will never dance. She has no talent.’ And I was destroyed. For two days, I cried. My parents didn’t know what to do with me. And then I said, No. I’m going to dance.”

At around 14, she auditioned for the School of American Ballet and got in, later performing with Ballet Society, a subscription-based company formed in 1946, in Balanchine’s “The Spellbound Child.” She was insistent on another point, too: “I just really was not his cup of tea.”

She referred to herself as “one of the numbers.” She never auditioned. “He knew that I was a very fast learner,” she said. “He knew he could always count on me. That no matter what happened, I would learn it. I’d get through it. And I think that was the main thing he respected about me. And I think he saw that I loved to dance.”

Walczak was also a sharp observer. (With the dancer Una Kai, she wrote “Balanchine the Teacher,” a jewel of a book examining the fundamentals that shaped the company’s first generation.) “What made him zero in on a dancer was not only the physical, the technical, the height, the look, whatever — and Suzanne Farrell’s the perfect example of it,” she said, referring to Balanchine’s muse of the 1960s and ’70s. “It’s the intangible, uncontrollable timing of her body.”