Ellen Stofan still feels a sense of awe when she walks through the National Air and Space Museum in Washington, D.C., even though she's been its director — the first woman ever to hold the position — since last spring.

"Whenever I look at things that have actually been in space, it never fails to give me goosebumps," she said in recent interview with Karlie Kloss for NBC's "Today" show.

Maybe that's not so surprising for someone who has spent a lifetime immersed in spaceflight. Stofan's father was a NASA rocket scientist, and she served as the space agency's chief scientist before being named director of the museum, whose holdings include Charles Lindbergh's "Spirit of St. Louis" and the Apollo 11 command module. (The museum is currently closed as a result of the government shutdown.)

But if Stofan is big on space, her goals in her high-profile job are surprisingly down to Earth.

“People have said to me, ‘it's important that you're the first woman director,’ and I want to say, 'no, of course not. Women are completely capable of doing anything,” Stofan told Kloss. “But it is important, because I want to inspire that girl that comes into this museum to say 'I could run the Air and Space Museum — but even more, I could be the first girl to walk on Mars.’”

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A 2017 report showed that while the number of women earning degrees in science has risen since the late 1990s, women still account for only about 20 percent of advanced degrees in physics and lag men significantly in obtaining advanced degrees in mathematics, computer science and other fields known collectively as STEM (for science, technology, engineering and math).

Eileen Pollack, a creative writing professor at the University of Michigan and author of "The Only Woman in the Room: Why Science Is Still a Boys’ Club," recalled her own experience as a physics student seeing the predominance of men at a NASA facility.

"If only I had seen someone who looked like Ellen Stofan in that control room, let alone found out she was NASA's chief scientist, I could have imagined myself among those scientists," Pollack told NBC News MACH in an email. "I always loved visiting the Air and Space Museum, but nearly all the early test pilots, astronauts and aerospace engineers were men. If I were to walk in now and see Dr. Stofan's photograph greeting me, the museum might seem far more welcoming."

Stofan’s own path from her Ohio childhood to planetary geologist at NASA wasn’t a clear one. “I didn't really think about myself as working for NASA because everyone that worked for NASA looked like my dad,” she said.

After studying geology at the College of William & Mary and earning her doctoral degree at Brown University, Stofan joined the space agency as a planetary geologist in 1991. She worked on a number of projects, including the Magellan spacecraft, a robotic probe that launched in 1989 to map the surface of Venus.

From 2013 to 2016, she served as NASA’s chief scientist, helping to hone the agency’s plans for launching humans to Mars and steering NASA’s broad portfolio of science programs, which cover everything from astrophysics to Earth science.

If Stofan’s career trajectory is a rarity among women, she’s hoping that will change. And she's driven not only by her hopes for young women but also by her admiration for the women who came before her. On one wall of her office hang photos of women who made their mark in aviation and spaceflight, including Jerrie Cobb, one of the “Mercury 13” female astronaut trainees in the 1960s; Bessie Coleman, the first African-American woman to hold a pilot’s license; and Amelia Earhart, the first woman to fly solo across the Atlantic Ocean.

“I look at this wall of women and say, these women laid a path for us,” Stofan said, “and all of us are just carrying on what they started.”

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