I spent the last two years researching women geniuses for my new book. Along the way, I encountered a few people who didn’t think the category existed at all.

It didn’t take long to discover the answer. Genius needs to be nurtured and recognized. Extraordinary women musicians have existed in every generation, but their potential was wasted because people were unwilling to see their talent.

A female Wolfang Mozart quite literally existed: Maria Anna, who was the sister of the brilliant and prolific composer. She might have been his equal if her talent hadn’t been left to molder.

Mozart’s early talent was expertly nurtured. When Wolfgang was young, his father, Leopold Mozart, took him on tour in Europe and introduced him to composers and musicians who advised and encouraged him. They helped him find positions that allowed his creativity to flourish.

Mozart’s older sister, Maria Anna, known as Nannerl, also had extraordinary talent: She performed on the harpsichord and toured with her brother when they were both young. Some reports say she was better than her little sibling and that he idolized and learned from her. At age 12, she was called one of the best musicians in Europe.

But it didn’t really matter. Once she hit her teens, her father deemed it inappropriate for her to perform anymore and sent her home to get married.

I suppose Maria Anna could have stood up to her father — and her entire society — and kept playing her music. Maybe that would have been a sign of true genius. But it’s unfair to demand that if you are an extraordinarily talented woman and want to be heard, you must also possess the stoic heart of a rebel. We never asked Wolfgang to take on the whole world. We just left him alone to do what he loved. His sister never got that chance.

Women of genius still have trouble being heard and nurtured and encouraged. Perhaps they aren’t told to go home and have babies, but they are left on their own to figure out how to combine family and genius, private and public. It’s not as obvious as in Nannerl’s day, but the pressures are just as real. All the political and social systems are neatly set against them.

And “amazing” is just the start, because, as she puts it, “there are unconscious biases that keep women from getting the right opportunities and the right stretch assignments.” A manager might not bring a woman to an important client meeting or put her on a career‐making case, for example, figuring that she’s going to get married and have children and leave anyway.

Women geniuses have often had to find work-arounds to get their talent noticed. Fanny Mendelssohn, a 19th century composer, published much of her work under the name of her brother, Felix, who explained that he was simply protecting her. As often happens when men are “protecting” women, it worked out rather well for him, too. He got all the credit for Fanny’s music, and some of it was notably better than his.

Fanny was prodigiously talented, and she and Felix shared tutors and music teachers when they were young. When Fanny was 14, her father, Abraham Mendelssohn, sent her a letter explaining that while Felix could go on and have a career in music.

It never occurred to Abraham or Felix that music was the root of her being. As with Nannerl, a genius woman was told that she had to give up what she loved for a man, and to fulfill, as Abraham wrote, “the only calling of a young woman … a housewife.”

Imagine telling a genius man that his talents as a child prodigy were all well and good, but now it’s time to suppress the talent and be a dad. He might turn to you and say, “Are you kidding? Why can’t I do both?”

Carol Anderson, professor of African American studies at Emory University, told me that smart women are always protecting themselves against the expected male backlash that comes from being too strong and too smart. Should there even be such a thing as too strong and too smart? Does it exist for men? It’s all part of what she called “the gendered language of deprecation” — which means that women often undermine themselves so as to sound nonthreatening. Or, as in the case of Fanny, they publish their work under a different name.

“Women are always aware of the threat of male violence,” she said, “and they worry about inciting it if they’re not sufficiently deferential to the male patriarchy.” To challenge social norms and question male dominance can literally be dangerous.

To one degree or another, smart women all hone a style of displaying expertise and authority without stepping too far from their expected roles. Genius isn’t a zero-sum game, but men sometimes treat it that way. As long as they hold the power to determine what is great, they’re not going to give any advantage to women.

When the world doesn’t want to listen to a girl — and you’re a girl — what is to be done? In addition to publishing under Felix’s name, Fanny came up with the very clever idea of holding Sunday afternoon musical salons at her home. She would invite 200 or more people. Because the performances were in her home and not on a public stage, they were deemed acceptable in society.

After her salons got attention, Fanny finally worked up her nerve, thumbed her nose at convention and published some pieces under her own name. Nobody collapsed in horror because a woman did great work. Instead, she got terrific reviews, and the brief period of acclaim that followed was, she said, the happiest time of her life. Sadly, in an ending that Leo Tolstoy might have written, she died soon after.

Nannerl didn’t fare much better. She got married, took care of extended family and died alone at age 78.

Our failure to nourish talented women has tragic personal consequences — but it’s tragic on a grander scale. Think about all the would‐be women math geniuses and computer scientists and composers who never had a chance to develop. Anderson, the professor, points out that you don’t build a powerful country by diminishing your work force.

“You ever hear that expression about cutting off your nose to spite your face?” she asks.

Men have rigged the system, but for country and self, women can’t ease up in the battle to change it.

Janice Kaplan is the author of “The Genius of Women: From Overlooked to Changing the World,” to be published Feb. 18 by Dutton, an imprint of the Penguin Publishing Group, a division of Penguin Random House