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and willfully and openly state that only some people can learn their subjects. Just last week I learned of two examples that are typical. A community college professor started her class by telling the students that only three of them would make it, and a high-school math teacher in my local school district announced to his eager fifteen-year-old students who were placed in his high-level math class: “You may think you are hot shit, but no one gets above a C in this class.” These are the words of elitists who revel in the low number of students who are successful in their classes, as they think it shows that they are teaching really difficult content. It is this sort of thinking and speaking to students that has kept so many amazing people from pursuing pathways that would have been rewarding for them. Such ideas harm people, and they harm the disciplines, because access is denied to the diverse thinkers who would have provided beneficial insights and breakthroughs in these fields.

      One of these thinkers was the incredible mathematician Maryam Mirzakhani. The story of Maryam’s life and work appeared in newspapers worldwide when she became the first woman in the world to win the coveted Fields Medal—the equivalent of the “Nobel Prize” for mathematicians. Maryam grew up in Iran and, like many others, was not inspired by school math classes. In seventh grade, Maryam was told by her math teacher that she was not good at math. Fortunately for the world, Maryam had other teachers who believed in her.

      At age fifteen things changed for Maryam when she signed up for a problem-solving class at Sharif University in Tehran. She loved mathematical problem solving and went on to study advanced mathematics. During her PhD studies she proved several previously unproved theories in mathematics. Her approach was different from that of many mathematicians, and her work almost entirely visual. The field would be narrower—less rich, visual, and connected—without Maryam’s contribution, one that could so easily have been lost if she had listened to the teacher who told her that she was bad at math.

      When Maryam came to Stanford, we found many occasions to meet and discuss mathematics learning, and I enjoyed chairing a PhD exam for one of her students. At age forty, she tragically died. The world lost an incredible woman, although her ideas will always live on and continue to broaden mathematics.

      The American Mathematical Society recently devoted the November issue of its journal to Maryam, and one of those reflecting on Maryam’s amazing contribution to mathematics was Jenya Sapir, the doctoral student whose thesis defense I chaired, now a mathematician herself. Here are her reflections on Maryam:

      Maryam would paint beautiful, detailed landscapes in her lectures. If she were giving a talk about concepts A, B, and C, she would not just explain that A implies B implies C. Rather, she would paint a mathematical landscape where A, B, and C lived together and interacted with one another in various complicated ways. More than that, she made it seem like the rules of the universe were working harmoniously together to make A, B, and C come about. I was often amazed by what I imagined her inner world to be like. In my imagination it contained difficult concepts from disparate fields of mathematics all living together and influencing one another. Watching them interact, Maryam would learn the essential truths of her mathematical universe.²²

      The world is filled with cases of people who think differently—often more creatively—and are dissuaded from pursuing careers in sports, music, academics, and many other fields. Those who persist despite the negative messages they receive often go on to achieve incredible feats.

      But how many are there who do not go forward, who believe negative judgments and who turn away from fields and dreams? One of the people who thought differently and received extensive rejection is the author of the Harry Potter series, J. K. Rowling, now the most successful author in history. Shortly after the death of her mother, she was at a very low point in her life; she was recently divorced, a single mother, living in poverty, but she focused on something she cared deeply about—writing. Rowling (also called Jo) sent her Harry Potter manuscript to twelve different publishers, all of whom rejected it.

      She began to lose confidence in her book when the editor at Bloomsbury Publishing sat down to read the book; she also gave it to her eight-year-old daughter. The young reader loved it and encouraged her mother to publish it. Rowling’s books have now sold over 500 million copies, and she is a role model for any who face rejection yet believe in their ideas. Today she actively works to end poverty and support children’s welfare. I love many of her words, but this is perhaps my favorite quote of all:

      It is impossible to live without failing at something, unless you live so cautiously that you might as well not have lived at all—in which case, you fail by default.

      The Problems of Giftedness

      The teachers, professors, and parents who maintain that only some people can learn subjects are all reflecting the misinformation of the fixed-brain era. It is perhaps not surprising that so many people still cling to the idea of fixed brains, as most of them lived during the years when this was all anyone knew. The fixed-brain myths have been devastating for students of all ages who have been written off in schools, classrooms, and homes, millions of children who have been made to believe they cannot achieve. But there is another side to this story as well. Fixed-brain thinking has also had negative consequences for the students who have been held up as being “gifted.” This may seem nonsensical—how can being labeled as gifted possibly harm anyone? I have already mentioned the research showing that the idea of giftedness—that you need some inherited gene to do well—is harmful for women and students of color, but how does it harm individuals who are given the label?

      A few months ago, I was contacted by a filmmaker who was making a film on giftedness with a social justice angle. That, I thought, sounded interesting, so I looked at the trailer he sent me. I was disappointed to find that his argument was that more students of color should be identified as gifted. I understand the motives for such a film, as there are serious racial disparities in gifted programs. But there was a larger issue at play, and that was the continued practice of fixed-brain labeling.

      I decided in those moments to make my own film, with the help of my youcubed team and an amazing filmmaker, Sophie Constantinou, from Citizen Film. I asked the Stanford students I knew to reflect upon their experiences of being labeled as “gifted.”²³ The twelve Stanford students who speak in the film give a consistent message—they received advantages, but at some costs. The students talk about feeling that they had a fixed thing inside them, and when they struggled, they thought it had “run out.” They say they learned that they could not ask questions; they could only answer other people’s questions. They say that they tried to hide any struggles, in case people found out that they did not have a “gift.” At the end a student named Julia strikingly says, “If I grew up in a world where no one was labeled as gifted, I would have asked a lot more questions.”

      The gifted movement has the worthy ideal of ensuring that high-achieving students get a rich and challenging environment, which I agree is needed. But they have done so by perpetuating an idea that some students are worthy of this because they have a fixed “gift”—like a present they have been given. Although the programs point out that some students need especially challenging material because they have reached an elevated point, they omit the fact that others can also reach that point if they work hard. The message is that some people are born with something that others cannot achieve. This, in my view, is damaging, both for those who get the idea they have no gift and for those who get the idea they have a fixed brain.

      One of the reasons that it can be damaging to receive the gifted label is that you do not expect to struggle, and when you do, it is absolutely devastating. I was reminded of this when chatting with my education students at Stanford last summer. I was explaining the research on brain growth and the damage of fixed labels when Susannah raised her hand and sadly said, “You are describing my life.”

      Susannah went on to recall her childhood, when she was a top student in math classes. She had attended a gifted program and had been told frequently that she had a “math brain” and a special talent. She went on to enroll as a math major at UCLA, but in the second year of the program she took a class that was challenging and that caused her to struggle. At that time, she decided she did not have a math brain after all, and she dropped out of the program. What Susannah did not know is that struggle is the very best process

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