Studying mathematics is an arduous undertaking, testing one's patience while learning new, complex concepts and one’s tolerance for frustration. This is common to all of us, and fortunately so, as it reminds us that we are not alone in this journey. We are however led to believe that there exist some exceptions in our world, some people who possess a certain knack for mathematics. For them, mathematical expressions come as naturally as brushstrokes to an artist. When we talk about these numerical artists, we think of Euler, Gauss, Newton, to name a few giants. While we humble mortals are quite certain of never attaining such intellectual heights as they did, we are capable of appreciating their talents from a content-based perspective thanks to our quantitative background. For the layperson, however, their encounter with the notion of the “mathematical genius” is often shaped by popular culture. But does this mathematician on the big screen correspond to the mathematician in the real world?

Good Will Hunting

If you haven’t watched this movie, or worse, haven’t even heard of it before, I would highly recommend you to do that right now. This movie is arguably the most famous portrayal of mathematical genius in cinema, and justifiably so. Our protagonist is Will, a janitor at MIT who lives a simple life, but has the potential for so much more. His hidden genius is revealed early in the movie when he solves a graduate-level math problem (from graph theory) left on a chalkboard in the middle of a hallway. For those interested, the actual problem isn’t that relatively difficult, but its main purpose is to serve as a narrative instrument. Will is encouraged to capitalize on his talent, but his stubborn personality and general rebellious nature, formed by experiences in his youth, are obstacles in realizing his potential. The narrative can thus be interpreted through a nature-nurture framework. Will’s innate and raw cognitive ability is not fully utilized due to the influences of his upbringing. 

Another point I want to touch upon is the “ordinariness” of Will’s life outside of his intellectual adventures. He’s not the awkward, shy geek typically associated with this stereotype. On the contrary, Will works a manual job, is comfortable navigating social contexts, even charming at times, and drinks a pint of beer with his friends in the evening. This is a conscious effort of the director and a big reason why the movie became so popular, as it challenges the conventional image of the troubled genius.

A Beautiful Mind

This next movie is a stark contrast to the previous one. Whereas Good Will Hunting situates its protagonist within an ordinary social environment, A Beautiful Mind depicts its central character, John Nash (whose Nash Equilibrium in game theory is named after), as increasingly detached from everyday society. The film fully leans into the trope of the brilliant, but troubled intellectual. It is based on the real life of John Nash, but heavily dramatized, as is to be expected from Hollywood. Here the emphasis lies not on the struggle of the individual versus his environment, but rather the struggle against himself. We see how a man, plagued with an ever-increasing mental illness, becomes increasingly unable to distinguish between perception and reality. Rationality is deeply entangled with psychological instability. The same mind capable of producing profound mathematical insight is also vulnerable to distortion and delusion.

Another distinction is that Nash clearly has an obsessive personality. Unlike Will, who is largely indifferent to his capabilities, Nash is constantly searching for patterns and underlying structures in his environment. This manifests itself in his engagement with cryptography, where his pursuit of hidden meaning gradually becomes all-consuming, eventually leading to a fallout with his wife Alice. This bears some resemblance with Good Will Hunting, where the protagonist also struggles to maintain a romantic relationship, although the underlying cause differs. In Will’s case, the breakdown stems from emotional avoidance rather than obsessive cognitive fixation. Having said that, the narrative functions of the relationships are the same; to provide a stable, real-world counterpart to the protagonists’ intellectual world. In the end, human connection prevails.

Different sides of genius

There are certainly many other depictions of our case study, not only in cinema, but pop culture in general. Across these portrayals, a clear pattern emerges: mathematicians are often framed through extremes of either social embeddedness or isolation, with their intellectual abilities closely intertwined with personal and emotional struggles. While Good Will Hunting emphasizes a more grounded, socially integrated individual and A Beautiful Mind leans into psychological fragmentation and withdrawal, both films rely on narrative choices that amplify certain traits for dramatic effect. As such, although they draw inspiration from real individuals, these characters do not fully correspond to the diversity and ordinariness of mathematicians in the real world. This does not necessarily diminish the quality of the films, but it is important to remain aware of these differences with the real world.