When she was about 14, Hillary Clinton says, she wrote to NASA to volunteer for astronaut training.

NASA’s reply was simple and definitive: No girls.

“It was the first time I had hit an obstacle I couldn’t overcome with hard work and determination, and I was outraged,” she would write in her book, “Living History.”

More than a half-century later, and after much hard work, much determination, and most of all, many, many obstacles — some undeniably of her own making — Clinton, 68, is no closer to space travel. She may have to settle for becoming the first female leader of the free world.

Her journey has been unlike any seen in American politics: great promise, excruciating setbacks, bitter scandal, stunning comebacks and especially reinvention — of her own life, and as a result, of the role of women in government. It’s one that has fascinated not just her country, but the world.

Think about it: Is any woman more recognizable on a global scale than Hillary Clinton? If Barack Obama was the presidential candidate who seemed to come out of nowhere, Clinton’s the candidate who seemed to come out of everywhere.

Americans first knew her as a governor’s working wife in Arkansas, then as the nation’s first lady — half of Bill Clinton’s “Buy one, get one free” bargain. Touched by scandal, she nonetheless emerged to become a hardworking senator, the first first lady to gain elected office. She was the presidential candidate who suffered a stinging defeat to Obama, but proudly claimed “18 million cracks” in the glass ceiling.

Then she reinvented herself again, becoming Obama’s secretary of State, traveling to 112 countries.

We knew her so well by then. Or not.

Perhaps it’s a question of layers, so many different roles. But there’s also a sense of impenetrability, exacerbated by Clinton’s penchant for secrecy — a characteristic that’s led to her greatest vulnerability now: the email scandal.

For the past 14 years, and 20 overall, Americans polled by Gallup have named Clinton their most admired woman in the world. But consider some other titles from over the years: Lady Macbeth. Washington insider. Robotic. Wildly ambitious. Congenital liar.

But also: Feminist heroine. Glass-ceiling breaker. The most prepared in the room. The most qualified presidential candidate ever. Loyal friend. Witty companion. Mom. Grandma.

“It’s an amazing life,” biographer Carl Bernstein says. “You could not make any of this stuff up.”

The ambition thing

“Saturday Night Live” has been turning out Hillarys for a good 25 years. There have been nine, including Miley Cyrus rapping in a bandeau. But there’s been one constant: Ambition.

“No, MINE!” blurted out Amy Poehler’s Hillary in 2008, of her thwarted road to presidential glory. More recently, Kate McKinnon’s Hillary moaned, “Why won’t the people just let me LEAD?”

Comedy aside, the ambition tag has dogged Clinton, as if it were a bad quality rather than a necessity. The satirical website The Onion captured the irony: “Hillary Clinton Is Too Ambitious To Be The First Female President.”

That gets a laugh from Melanne Verveer, Clinton’s chief of staff as first lady.

“If a guy is described as ambitious, it’s a noble attribute,” Verveer says. “But if a woman is ambitious … it’s a pejorative.”

Champion for women

Hillary Rodham was already blazing a trail in 1969, the first student chosen to address a Wellesley commencement. She delighted classmates with an on-the-spot rebuke to the previous speaker, whose comments the grads found condescending to women.

It’s been a frustration to Clinton’s campaign that young Democrats haven’t responded more enthusiastically, with many attracted to the populist message of Bernie Sanders (who is six years her senior).

“Young people today want to be part of something bigger … but they don’t understand how much she shares those aspirations of theirs,” Verveer says.

A key moment in Clinton’s journey came in 1995, with her famous Beijing declaration: “Human rights are women’s rights, and women’s rights are human rights.”

Yet her image as a champion for women has been complicated by her, well, complicated marriage — she’s gotten both sympathy and blame for staying with her husband.

Robotic or human?

“I am not a natural politician, in case you haven’t noticed,” Clinton offered recently.

But those who’ve watched her up close say she’s an excellent communicator, and friends always say she’s relaxed, funny, witty. Wellesley classmates say they can’t understand the disconnect between public and private Hillary.

At their 35th reunion, Nancy Herron performed a stand-up routine skewering Clinton — even her famous pantsuits.

“She sat there and just laughed her head off,” Herron says. “Afterward, she gave me a hug, and said, ‘We need to take you on the road!’ ”

The truth issue

Fair or not, dishonesty is a theme woven into the Clinton story. “The most difficult thing Hillary Clinton has to deal with right now,” said Bernstein, author of “Hillary in Charge,” ”is her difficult relationship with the truth.”

Writer Gail Sheehy attributes that difficulty to years of fending off attacks.

“You could call it denial,” said Sheehy, author of “Hillary’s Choice.” ”It’s a defense mechanism she has used a great deal.”

The issue has never been more important. What the email mess shows, Bernstein says, is “this fierce desire for privacy and secrecy that seems to cast a larger and larger shadow over who she really is.”

Who she really is. There’s that question again. Is it fair?

Former Rep. Pat Schroeder thinks not. “What more do you want to know?” said the former congresswoman, who tested out her own candidacy decades ago. “Do they want some kind of a confession?”

Herron believes that we don’t subject male candidates to the same scrutiny. “We expect her to let her hair down, to talk about her failures and self-doubt or something,” she says.

“You know what? She’s not like that! Let her be who she is.”