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Imagine being so beautiful that no one would let you be smart. That's the sad story of Hedy Lamarr, the subject of Alexandra Dean's debut feature documentary, Bombshell. After causing a splash in feature films like Ecstasy and Algiers, Lamarr became known as "the most beautiful girl in the world." Lamarr was a public figure with a secret: She was a creative genius who patented a "secret communication system" that is the basis of the Wi-Fi, Bluetooth, satellite, and military technology millions of people use to this day. But few people ever really took her seriously; she was just too beautiful.

"What shocks me about Hedy's story is that I feel like she's a woman from today who wandered accidentally into that time period," Dean said at a panel after a screening of the documentary at the Tribeca Film Festival. "Unfortunately, I think she was punished a little bit for that...she was so bold." Over the past couple of decades, details about Lamarr's life as an inventor have emerged. But thanks to some unearthed interview tapes—discovered behind a trash can, naturally—Bombshell lets Lamarr tell her own story, alongside admirers and narrators like Diane Kruger, Mel Brooks, and Lamarr's family.

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Bombshell is often pure fun—it doesn't have much choice, given the robust bites its subject took out of life. When she was just a teenager, she appeared nude and performed the first onscreen female orgasm in Ecstasy, a 1933 film that the pope denounced and Hitler banned. Later in her life, she also produced three films at a time when women just didn't do that.

"She was too old at 40," said Susan Sarandon, an executive producer of the film, during the panel. "They were phasing her out at 40. I did Bull Durham at 40! I remember when I came in to the business, everybody did say, 'Don't let anyone know you have kids. You'll be lucky if you make it to 40 and still be able to be sexual and sensual.'" Sarandon, who recently played Bette Davis in FX'sFeud, likened Lamarr to Joan Crawford. "The thing that gave Bette longevity and that has helped me age is that I thought of myself as a character actress. Bette Davis thought of herself as a character actress...but Joan Crawford was the most beautiful girl in the world. So her transition was more painful."

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Indeed, when we look at the woman behind the scenes, a melancholy story plays out. After a daring escape from her first, very jealous husband and impending Nazi rule in Austria (she disguised herself as a maid and left the house in the middle of a party), she was discovered by Louis B. Mayer of Metro-Goldwyn-Mayer in London. Quickly sucked into the studio system, she was worked like a racehorse, appearing in several forgettable and even some risible films. Ultimately, the Hollywood life wasn't enough for her—she had a small drafting table installed at home and worked on her true passion there at night: inventing.

Lamarr may be remembered for her show-stopping face and the salacious details of her six marriages and love affairs. But we should instead remember her as the woman who suggested that Howard Hughes change the shape of airplane wings—from rectangular to something based on the natural shapes of fish fins and bird wings.

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And her most astonishing achievement? At the height of the WWII war effort, with her inventing partner, the avant garde pianist George Antheil, Lamarr came up with the idea for a radio-controlled torpedo. It incorporated the groundbreaking concept of frequency hopping, which would allow missiles to go undetected.

Eventually, her invention would be used during the Cuban Missile Crisis, and would serve as the groundwork for wireless technologies we all use today. But at the time, the navy didn't care for her idea, and the patent was thrown into the vault. Lamarr was encouraged instead to entertain the troops and assist in fundraising efforts. Thanks to subsequent professional failures and personal problems—including an encounter with the infamous Dr. Feelgood, who dosed her up with "vitamins" that were really methamphetamines—her life took a sharp downturn. The actress lost everything she had, ending up on social security.

Towards the end of her life, Lamarr became a recluse. "I want peace," she said in an interview. After her chaotic life, no one could begrudge her that. But her innovative mind and pioneering spirit should stand alongside her acting prowess and, yes, that face. Lamarr liked to read a Kent M. Keith poem to her son over the phone. "What you spend years building overnight may be destroyed," it says. "Build it anyway."

Bombshell is screening at the Tribeca Film Festival.