MIKE NICHOLS claims he called Marilyn Monroe to work on a scene.
“Are you sure you weren’t hitting on her?” I asked.
“I wouldn’t have dared dream of it,” he replied.

It was the mid-1950s, and they were both taking an acting class in New York with Lee Strasberg. Nichols recounted his conversation with the woman with the familiar breathy voice:
“The phone rang and somebody said, ‘Hello,’ and I said, ‘Hi, is Marilyn there?’ and she said, ‘No, she’s not,’ and I said, ‘Well, this is Mike. I’m in class with her. Could you take a message?’ And she said, ‘Well, it’s a holiday,’ because it was the Fourth of July weekend, and that, to her, was an excuse for not taking a message for herself.”

No one ever said Marilyn wasn’t complicated.

Nichols directed the Tony Award-winning revival of her third husband’s play, “Death of a Salesman.” I interviewed him for a BBC radio show based on a column I wrote for The Times about how we have devolved from Marilyn’s aspirational attitude toward knowledge, in which she wanted to collect great books and meet authors and intellectuals — even marrying one — to Sarah Palin’s anti-elitist scorn about reading and intellectuals.

Nichols surprised me when he said he was present at what he dryly calls the “historic moment” in May 1962 when Marilyn sang “Happy Birthday” to Jack Kennedy, who was turning 45. Marilyn was wearing that shrink-wrap, sheer Jean Louis gown ablaze with rhinestones — “skin and beads,” she called it. Nichols and Elaine May were also performing that night in Madison Square Garden, not that anyone remembers.

“I was standing right behind Marilyn, completely invisible, when she sang ‘Happy birthday, Mr. President,’ ” Nichols said. “And indeed, the corny thing happened: Her dress split for my benefit, and there was Marilyn, and yes, indeed, she didn’t wear any underwear.”

At a party afterward, “Elaine and I were dancing, and Bobby Kennedy and Marilyn danced by us, and I swear to God the conversation was as follows — ”

Here Nichols put on, first, a feathery voice and then a nasal one:

“ ‘I like you, Bobby.’
“ ‘I like you too, Marilyn.’ ”

The famous director has worked with many famous beauties. So I asked him, as we mark the 50th anniversary of Marilyn’s death, if he could explain her astonishing staying power.

“I think that the easy answer might be that she had the greatest need,” he said. “She wasn’t particularly a great beauty, that is to say, Hedy Lamarr or Ava Gardner would knock the hell out of her in a contest, but she was almost superhumanly sexual.”

Feminism has come and gone, and women now routinely puff their lips, inflate their chests, dye their hair and dress with sultry abandon. But Nichols said Marilyn’s heat went deeper, with a walk, a look and movements that were an “out-and-out open seduction right in front of everyone.”

Arthur Gelb, the former Times managing editor, likes to tell how he won a $10 bet as a slightly inebriated rewrite man in the ‘50s when he reached out and, much to her annoyance, touched Marilyn’s flawless porcelain back as she dined with friends at Sardi’s.

“When she walked, it was as though she had a hundred body parts that moved separately in different directions,” Gelb told me on the BBC show. “I mean, you didn’t know what body part to follow.”

Wherever I travel in the world, I run across the luminous image of the heartbreaking and breathtaking sex symbol who was smart enough to become the most famous “dumb blonde” of the 20th century. Marilyn, her white pleated halter dress flying up over the New York subway grate, is as deeply etched in the global imagination as Audrey Hepburn in a black Givenchy dress at Tiffany’s.

Starting as the 1948 Castroville, Calif., artichoke queen, Marilyn was a genius at self-creation, high gloss over deep wounds. “Marilyn’s like a veil I wear over Norma Jeane,” she said.

Lois Banner, a professor of history and gender studies at the University of Southern California, hails the star in her new book, “Marilyn: The Passion and the Paradox,” as a proto-feminist who had to swim upstream past a mentally ill mother, 12 foster homes, a stutter, sexual abuse as a child, sexism as a star, manic-depressive cycles, addiction, Joe DiMaggio’s abuse and Arthur Miller’s condescension. “She is the child in all of us,” Banner writes, “the child we want to forget but can’t dismiss.”

Half a century after Marilyn was found on Aug. 5, 1962, in her Brentwood bedroom, nude, holding her phone, soaked in drugs, she continues to bewitch: her death at 36 and the sketchy cover-up; her tempestuous marriages to a famous baseball player and famous playwright; her role, with Jack and Bobby Kennedy, in the most intriguing film noir triangle of all time.

She gazes wistfully from the latest People, beside Rob and Kristen, with the headline, “Was Marilyn Murdered?”

“Could the iconic bombshell,” USA Today asked, “be any more alive?”

She made $27 million last year, gobs more than she ever earned in life. She was the poster girl at Cannes, a festival she never attended. And her time in England making “The Prince and the Showgirl” was the subject of a movie that got two Oscar nominations, even though the golden girl never won a gold statuette herself.

There’s a fresh cascade of books, photos, Twitter messages, Blu-ray box sets, Marilyn Monroe Cafes, Marilyn nail salons, and a MAC makeup collection.

NBC’s “Smash” is set behind the scenes of a Broadway show based on Marilyn’s life; Nicki Minaj has a song called “Marilyn Monroe,” and the documentary “Love, Marilyn” will have its premiere at the Toronto Film Festival next month. There had even been talk about revivifying the sex kitten for a hologram show.

While making her last movie, “Something’s Got to Give,” Marilyn posed nude for a young photographer, Larry Schiller, hoping to ratchet up her $100,000 salary to Elizabeth Taylor’s million-dollar territory for “Cleopatra.”

Schiller wrote in Vanity Fair that he saw the confidence that spurred Marilyn to become one of the first stars to create her own production company. “There isn’t anybody that looks like me without clothes on,” she laughed.

He also saw her dark companion, insecurity. “Is that all I’m good for?” she keened about nudity.

Yet Schiller told The Associated Press that “it’s women that have kept Marilyn alive, not men.” He says teenage girls flock to see gallery shows, and that the photos selling now accentuate her humanity, not her anatomy.

“I think,” he said, “people want to see her now as a real person.”