In 1939, a first-year doctoral student at UC Berkeley named George Dantzig, arrived late to class. His professor, famous statistician Jerzy Neyman, had written two statistics problems on the blackboard. Dantzig quickly jotted them down, assuming that they were homework problems. A few days later, Dantzig turned in the problems late to Professor Neyman, apologizing for the overdue assignment. The problems had seemed “a little harder to do than usual.” Six weeks later, an ecstatic Professor Neyman knocked on Dantzig’s door. As it turns out, the problems weren’t homework at all. They just so happened to be two famous unsolved problems in statistics. And Dantzig had solved both of them.
The story of the solved “homework problems” would later inspire an iconic scene in the 1997 academy award winning film, “Good Will Hunting,” centered on the story of Will Hunting, a 20-year-old South Bostonian janitor who is an unrecognized math prodigy. In the scene, a Massachusetts Institute of Technology math professor challenges his students to solve an incredibly difficult math problem, which he writes on a hallway blackboard. Will, who works as a janitor for MIT, comes across the problem and solves it in a matter of minutes. The next day, when the professor calls for the reveal of the mystery student who solved the problem, no one comes up. Puzzled, the professor puts up another challenging problem, which took two years to be solved. Once again, Will sees the new problem and solves it with ease, however this time, he gets caught. The rest of the movie’s trajectory follows a beautiful journey of Will learning to cope with the consequences of his traumatic childhood while exercising his intellectual capability.
In the film, Will, played by a young Matt Damon, is portrayed as naturally intelligent; someone who is gifted with genius. Oftentimes, this is how intelligence is depicted by the media, as a trait that can only be genetically inheritable. Will was born a “genius.” Dantzig was “destined” to make mathematical breakthroughs. However, according to renowned psychologist and Stanford professor Carol Dweck, this view can actually be quite harmful. Curious to learn what differentiated kids who backed away from challenges and were quick to give up from kids who actively challenged themselves and persisted despite the obstacles, Dweck spent a good portion of her career studying the mindsets of children when facing tough challenges. Her study on the topic boiled the answer down to two distinctions: fixed mindset and growth mindset.
Oftentimes, this is how intelligence is depicted by the media, as a trait that can only be genetically inheritable. Will was born a “genius.” Dantzig was “destined” to make mathematical breakthroughs.
A child who possesses a fixed mindset sees their abilities as set in stone. They are either good at math or not; either talented at singing or not. An individual’s skills are only of a certain amount, and if they face difficult challenges, their limited skills are put into question. In a TED Talk given by Dweck, she mentioned that with a fixed mindset, children are “gripped in the tyranny of now.” Her studies showed that students with fixed mindsets during tests showed more signs of cheating and comparing themselves with others who did worse than them. The children were desperate to salvage their “inherent” skills and talent. As Dweck puts it in her bestselling book, “Mindset,” “From the point of view of the fixed mindset, effort is only for people with deficiencies…. If you’re considered a genius, a talent, or a natural—then you have a lot to lose. Effort can reduce you.” In the person’s mind, they’ve lost the genetic lottery, and thereby, don’t have much incentive to try. It can seem pointless to make strong attempts at learning to play the cello when one is convinced that they don’t have any musical talent. Why try learning computer science when you know you’re bad with computers? This rigid and demeaning mindset hinders the expansion of our capabilities.
On the other hand, a growth mindset is believing that abilities can be developed through effort and persistence. A child who has a growth mindset is eager to undergo challenges to engage in new learnings. They are aware that they are capable of growth. As written in Dweck’s book, people with growth mindsets “believe a person’s true potential is unknown (and unknowable); that it’s impossible to foresee what can be accomplished with years of passion, toil, and training.” With this hope of greater potential, people become more willing to devote their time to improving their skills in various areas. During her study, Dweck conducted a CT scan on childrens’ brains and saw that the brains of kids with growth mindsets lit up with activity. When taking on new challenges and problems, the brain’s neurons make new and stronger connections, ultimately making the individual smarter.
Growth mindset is present in people such as Dantzig. For starters, as a child, Dantzig was reared to constantly challenge himself and grow in his mathematical capabilities. His father, a mathematician, would challenge him with tough problems in projective geometry. In her study, Dweck emphasizes that the role of parents in fostering their childrens’ mindsets is crucial. Many of us may have grown up hearing consoling phrases from our parents such as, “It’s OK if you’re not good at science; not everyone is good at it.” It’s these types of words that shape our minds into thinking that we are not cut out for certain skills and that there’s no use in trying to gain them. Instead of fostering this restrictive attitude, Dweck proposes that parents “praise the effort that led to the outcome or learning progress.” Rather than praising intelligence or talent, parents should praise parts of the process such as effort, strategies and improvement. This allows children to see that their efforts are important and can lead to growth, thereby encouraging them to continue challenging themselves.
Many of us may have grown up hearing consoling phrases from our parents such as, “It’s OK if you’re not good at science; not everyone is good at it.”
Dantzig’s willingness to put such a high level of effort into a couple of homework problems shows that Dantzig genuinely cares about his learning and likes to challenge himself. Despite the immense difficulty of the problems, he persisted through the challenge and ultimately succeeded. Even when it went past the deadline, he still continued to work on them. He could have easily given up and not turned in the problems at all. However, he was willing to deal with the full challenges of the problems.
However, if Dantzig had known that those two statistics problems weren’t homework problems, would he still have been able to solve them? Would he have even attempted to solve them in the first place? According to Dantzig himself, the answer is no: “If I had known that the problems were not homework but were in fact two famous unsolved problems in statistics, I probably would not have thought positively, would have become discouraged, and would never have solved them.” Therefore, Dantzig’s story may not be a complete display of a growth mindset after all.
When Dantzig was working on the problems, he was under the illusion that they were for homework. This illusion tailored his mind to think that the problems “had to be solved” and that they were solvable by doctorate students such as himself. Here, we get the essence of a fixed mindset. As Dantzig said himself, he wouldn’t have been able to solve those problems if he knew that they were actually the famous unsolved statistics problems. Dantzig may not have even put in the effort to tackle the challenging problems simply because he was still a student and didn’t believe he had the capacity to do so. In this way, he would’ve limited himself.
Dantzig’s case introduces a nuance to Dweck’s label of fixed and growth mindset: People can switch between both mindsets depending on the situation or the task. In other words, a person doesn’t always one-dimensionally either have a fixed mindset or a growth mindset. As Bill Gates, a strong advocate of Dweck’s work, writes in a review of her book, “My only criticism of the book is that Dweck slightly oversimplifies for her general audience. … most of us are not purely fixed-mindset people or growth-mindset people. We’re both. When I was reading the book, I realized that I have approached some things with a growth mindset (like bridge) while other things in a fixed mindset (like basketball).” With Dantzig’s case, we can see that one can engage in both fixed and growth mindsets depending on the situation.
As Bill Gates, a strong advocate of Dweck’s work, writes in a review of her book, “My only criticism of the book is that Dweck slightly oversimplifies for her general audience. … most of us are not purely fixed-mindset people or growth-mindset people. We’re both.”
Thus, we can conclude that the first step to fostering a growth mindset is recognizing the areas in which we have fixed mindsets. It’s also crucial to be aware of how the media can trick our minds into becoming more and more fixed. Take “Good Will Hunting,” for instance. Will isn’t depicted as someone who worked exceedingly hard to be a math whiz. He reads lots of books, but everything else comes with that brain of his. Many films and news stories follow this portrayal: They glorify “special” individuals for their almost superhuman intellect, making consumers of the media feel all the more incapable. And the problem is only heightened by the fact that we crave stories such as this, stories of geniuses who solve crazy problems and save the world. We idolize people such as Albert Einstein and Stephen Hawking for their intelligence and oftentimes disregard their perseverance and hard work that contributed to their great success. This mindset isn’t fair to Einstein and Hawking, and it isn’t fair to ourselves. After all, we can be a lot more capable than we think.
Back in 2008, Malcolm Gladwell wrote a piece in the New Yorker about how great discoveries are often “in the air,” and it doesn’t take a single genius to discover it. He uses an example about Alexander Graham Bell and his extraordinary invention of the telephone. He writes that while Bell is often credited for inventing the telephone, another man by the name of Elisha Gray had been working on the telephone around the same time. In fact, they filed notice with the U.S. Patent and Trademark Office in Washington, D.C. on the same day. Sadly, for Gray, only Bell became widely recognized as the inventor of the telephone. With this example, Gladwell makes the point that “Good ideas are out there for anyone with the wit and the will to find them.” He deconstructs the idea that solitary geniuses are destined to make certain discoveries.
However, because our minds are so tailored to crediting a single genius, we become suspicious when others make similar breakthroughs. We instinctively question the credibility of their work. As Gladwell writes, “We’re reluctant to believe that great discoveries are in the air. We want to believe that great discoveries are in our heads—and to each party in the multiple the presence of the other party is invariably cause for suspicion.” However, if numerous other people are just as capable of making the same discoveries, then it must mean that our romantic notion of a “genius” is false. Near the end of his article, Gladwell refers to a notable essay written in the 1960s by sociologist Robert K. Merton. Merton writes, “A scientific genius is not a person who does what no one else can do; he or she is someone who does what it takes many others to do. The genius is not a unique source of insight; he is merely an efficient source of insight.”
While there may be people out there in the world who have brains like Hunting, we shouldn’t rely on genetics for knowledge and talent. No one, not even the smartest individual, can get anywhere in life without the ability to face challenges and to persevere through them. In the words of Dweck, “The world of the future is going to be about taking on ill-defined, hard jobs that keep changing. It’s going to favor people who relish those challenges and know how to fix them.”And so that’s why we need to open and train our minds to remember:
George Dantzig put in a lot of effort to solve those problems,
Will Hunting is Hollywood made
and that for every Alexander Bell, there’s an Elisha Gray.