Between them, they run one of the world’s most prestigious universities, one of its biggest companies and one of its most powerful institutions. It’s hard to imagine anyone telling Christine Lagarde, the head of the IMF, Drew Faust, the president of Harvard, or Indra Nooyi, CEO of Pepsi, that they couldn’t succeed because of their gender – but that’s precisely what happened.

In different situations, these three women were effectively told the same thing: that girls and women shouldn’t aspire to the same goals as boys and men. It’s a message that’s stubbornly pervasive in every society in the world, reinforcing a global gender gap. Unsurprisingly, Lagarde, Faust and Nooyi refused to listen to it. Here’s how they reacted when faced with overt sexism and dubious advice.

Long before she was appointed managing director of the International Monetary Fund in 2011, Lagarde started her career as a lawyer. CNN reported her telling the following story:

“It was when I applied to the biggest law firm in Paris and I was told that I would be a great recruit and that I would be given good work to do – but that I should never expect to make partnership because I was a woman.

“I thought to myself: ‘You don’t deserve me, I’m going.’ And I had that sense of extraordinary freedom, walking down the staircase and thinking to myself: ‘What would I do in this firm? Why would I work with that kind of attitude?”

Rather than just “making partnership”, Lagarde went on to became the first female chair of the international law firm Baker & McKenzie, the first female finance minister of a G8 economy (and ranked the best in the Eurozone by the FT in 2009), and the first woman to head the IMF. Here she is on the stage at Davos earlier this year, discussing the outlook for the global economy in 2016:

The historian, prize-winning author and president of Ivy League bastion Harvard was raised in the south of the United States in a setting that didn’t exactly propel her along the path to greatness. In a video interview on closing the gender gap for the World Economic Forum, she described the attitudes she encountered as a child:

“When I was a small child growing up in Virginia what was expected of me was – not very much. My mother thought the best outcome would be if I found a suitable husband and raised a family, and she often said to me, when I chafed under restrictions that differentiated me from my three brothers, ‘It’s a man’s world sweetie, and the sooner you recognise that the sooner you’ll be happy.’”

Needless to say, her aspirations differed from those of her mother. Appointed president of Harvard in 2007, she is the author of six books, the most recent of which, The Republic of Suffering, was a finalist for the Pulitzer prize.

In a recent lecture, Educate Women, Change the World, Faust made the case for closing the gender gap not just on the grounds of fairness, but for economic strength.

“Every nation’s long-term competitiveness depends on how well it educates and brings into play its women and girls.”

A future where everyone can fulfill their potential, regardless of their gender, and where the appointment of a woman at the helm of a university raises zero eyebrows? We’ve got a long way to go.

In 2001, Indra Nooyi had just received the news that would make any parent proud. The now-CEO of Pepsi had told her that she had been appointed president and chief financial officer of the famous brand. Elated and exhausted, at 10pm she went home after a long day to tell her family. In a frank Atlantic interview, she explains what happened next:

“‘Mom, I’ve got great news for you.’ She said, ‘let the news wait. Can you go out and get some milk?’ I looked in the garage and it looked like my husband was home. I said, ‘what time did he get home?’ She said ‘8 o’clock.’ I said, ‘Why didn’t you ask him to buy the milk?’ ‘He’s tired.’ Okay. We have a couple of help at home, ‘why didn’t you ask them to get the milk?’ She said, ‘I forgot.’ She said just get the milk. We need it for the morning. So like a dutiful daughter, I went out and got the milk and came back.”

As well as buying the milk, Nooyi continued to climb the ladder. In 2006, she became the fifth CEO in Pepsi’s history, while in 2008, she was also appointed chair of the US-India Business Council.

Stories like this might be inspiring; but they are also relatively rare. According to the World Economic Forum’s Future of Jobs report, the proportion of women in positions of power dwindles all the way to the top: only around one in ten CEOs are women. From lingering beliefs about who should be the breadwinner – and who should be the milk-buyer – to workplace structures that no longer fit with the reality of working families, there are a whole host of factors still holding women back.