Popular entertainment stories about prodigies tend to follow certain common threads. The prodigy is smart but poorly socialized and sometimes a bit of an asshole. If well-meaning people can talk him off that perch, we get a happy ending (“Good Will Hunting”). If on the other hand a controlling parent or guardian figure is allowed to take over, the prodigy is more likely than not to crash and burn (“Shine”).

“Gifted,” the story of a young math prodigy named Mary and her mathematically gifted family, draws on both of these story lines, setting up a competition between the controlling figure (Mary’s grandmother Evelyn) and a well-meaning person (Mary’s uncle Frank). It’s funny and watchable. Mckenna Grace and Chris Evans have great chemistry. It’s also a film about three generations of female mathematicians, written and directed by men, with the participation of four mathematical consultants, all of them male. And it’s a missed opportunity. It’s not that men should not make films about women: I believe they absolutely should. It’s not that I would have preferred a social treatise about gender and math: I get my fill of that elsewhere. But I think that it was possible to go much deeper, dig through the clichés and explore a much more interesting territory. That road was left not taken.

I must start with disclosure: I was a math prodigy back in the day. I skipped a few grades, entered university at the age of 15 which was 4 years ahead of the normal schedule, and participated in math olympiads, where my highest accomplishment was being on the Polish team at the 1981 IMO in Washington. It’s not necessarily that much as prodigies go – I did not win any medals at the IMO, nor did I earn a Ph.D. by the age of 20 as some do – but then I was just a small town prodigy in backwater country and so you must calibrate your expectations accordingly. My parents couldn’t drive me to university classes or special gifted programs while I was in school. No such things were available where I lived, and in any event, my parents worked more than two full-time jobs between them, including both paid employment and maintaining a 5-person household at a time when food shortages were common and few Western style conveniences were available. Nor did they have a car.

I’m saying all this not to brag or complain, but to explain my interest in the matter and state my qualifications to discuss it. I’m aware that other folks may be less particular about such movies than myself. Public images of mathematical women continue to be scarce. Given how many Hollywood films still fail the Bechdel test, I do appreciate it when two women have a conversation that not only is not about a man, but also extends to mathematical research and female ambition. But if you’re looking for a review that only comments on the actual film and refrains from speculating on what could or might have been if someone else had made a different one, this is not it. I’m laying claim to my own territory which they have breached. I know the ground here. I talk to the birds and the snakes. I’ve learned my way around the place many times over. What about you? Are you interested in learning?



We can always start by defining our terms. Who is a “prodigy”? Do we make that evaluation based on promise or on accomplishment? What level of either must we see before we invoke the designation? This matters, especially in the context of female prodigies, because:

“Men are often judged on their potential, but women are judged on their achievements,” Williams explains, adding that women have to provide more evidence of competence to be considered as competent as their male colleagues. What’s more, “women’s mistakes tend to be noticed more and remembered longer, but women’s successes tend to be attributed to luck.” Williams calls this pattern “prove it again.” Women literally need to prove themselves over and over again, where a similarly situated male colleague does not, she explains. The obvious solution to this problem would be for women to engage in serious self-promotion, by broadcasting their accomplishments and minimizing their faults. But, says Williams, self-promotion has its pitfalls. No one likes a braggart, especially if she is a woman. Instead, coworkers expect women to be modest and community-minded.

Historically and socially, this is supported by well established patterns of thinking about talent and gender. In an earlier post I quoted Linda Nochlan’s critique of the notion of “the lady’s accomplishment”:

In contrast to the single-mindedness and commitment demanded of a chef d’ecole, we might set the image of the “lady painter” established by 19th century etiquette books and reinforced in the literature of the times. It is precisely the insistence upon a modest, proficient, self demeaning level of amateurism as a “suitable accomplishment” for the well brought up young woman, who naturally would want to direct her major attention to the welfare of others–family and husband–that militated, and still militates, against any real accomplishment on the part of women. It is this emphasis which transforms serious commitment to frivolous self-indulgence, busy work, or occupational therapy, and today, more than ever, in suburban bastions of the feminine mystique, tends to distort the whole notion of what art is and what kind of social role it plays. In Mrs. Ellis’s widely read The Family Monitor and Domestic Guide published before the middle of the 19th century, a book of advice popular both in the United States and in England, women were warned against the snare of trying too hard to excel in any one thing: “It must not be supposed that the writer is one who would advocate, as essential to woman, any very extraordinary degree of intellectual attainment, especially if confined to one particular branch of study. ‘I should like to excel in something’ is a frequent and, to some extent, laudable expression; but in what does it originate, and to what does it tend? To be able to do a great many things tolerably well, is of infinitely more value to a woman, than to be able to excel in any one. By the former, she may render herself generally useful; by the latter she may dazzle for an hour. By being apt, and tolerably well skilled in everything, she may fall into any situation in life with dignity and ease–by devoting her time to excellence in one, she may remain incapable of every other.”

Rebecca Traister has more in “All The Single Ladies”:

The American medical establishment built on European pronouncements to rationalize their recommendations to keep women’s lives small, confined, and attached to men. In his 1873 Sex in Education; or a Fair Chance for the Girls, Harvard professor Edward Clarke argues that the female brain, if engaged in the same course of study as the male, would become overburdened and that wombs and ovaries would atrophy.

Today, these attitudes might not be expressed in the same manner, but they still exist. The “greater male variability” hypothesis is alive and well. There’s no shortage of talking heads and internet commenters assuring us that women are innately uninterested in demanding careers and must prioritize domesticity to feel happy and fulfilled. Hollywood films serve up stories of high-achieving professional women who are miserable, psychologically damaged, and/or must be saved from themselves by a man with a good heart.

Mary comes to us as accomplishment personified, studying differential equations at the age of 7 and impressing Harvard professors with her command of multivariable calculus. Every teacher and mathematician who comes into contact with her recognizes her immediately as exceptionally gifted. Even when the adults disagree on what would be best for Mary’s development, her talent itself is never in question. I’m just going to be very blunt here and say that, given the circumstances of Mary’s upbringing, I don’t believe that any of this is possible.

Real-life prodigies, at least those who show up for evaluation straight from homeschooling, are more difficult to judge. Their patchwork knowledge base, growing in spurts according to what attracts the child’s attention at the moment, obeys no organizing principles that would be comprehensible to anyone else. Given two things that are normally taught together in school, the prodigy might know one very well and another not at all. She might excel at calculating integrals but then get stumped by third-grade notation that had never been explained to her, or by a multiple-choice test in a format that she had never practiced. She might be able to solve a difficult math problem but then have trouble explaining how she did it, the latter being a skill that requires practice with other people’s participation and feedback. (“Gifted” almost goes there, in one scene that had me wishing for more, but then the misunderstanding is cleared up quickly and Mary’s successful streak remains unbroken.) Think of Ramanujan, whose letters to English mathematicians were initially met with summary dismissal, and whose notebooks took many years to decipher even after Hardy hailed him as a genius.

There is no deep psychological mystery here, just a simple fact about autodidacts. A wise person once told me the story of a man who tried to learn the basics of karate from books, then came to a club for testing. His basic techniques were comparable to those of other white belts testing for yellow. However, when he was asked to perform the kata heian shodan, he returned to the “ready” position after every technique instead of stepping continuously from each punch or block into the next one as the kata requires. The books had never addressed that particular point. This is something that would have been clarified by attending a single class in a club, or even merely watching one. Today, there are videos; even so, the autodidact might skip them, assuming (incorrectly) that they only duplicate the books. No matter how exceptionally talented you might be, it is very difficult to master something in the absence of contact with living, breathing practitioners of the discipline. It’s not impossible, but it does take sustained and systematic work over many years if not decades. Even then, such people still come off differently from those who have had formal training.

A child prodigy is often self-taught, improvising a study program as she goes, with the temperament, intellectual maturity, and broad perspective of the small child that she is. Mary would certainly be an autodidact. We are given to understand that Frank taught her a few speed-computation algorithms, but even if he had been capable of teaching her calculus as well (he’s not a professional mathematician), we do not expect that he would have chosen to do so. It is also implied that Mary did not even have access to textbooks or full use of a computer prior to meeting her grandmother Evelyn, which had me wondering why Mary should need a gifted program or indeed any kind of school at all if she’s doing that well on her own. I understand and accept the general principle that if a film about mathematicians gets the human part right, it can be forgiven for not being 100% accurate in its depiction of mathematics. Here, though, the two are hard to separate. If a self-taught prodigy were to report for evaluation as Mary does, a flawless picture of well-schooled accomplishment, I have no doubt that every teacher’s response would be unequivocally enthusiastic. In mathematics, we refer to such implications as vacuously true.

In real life, there would be ample grounds for doubt, suspicion and disbelief. Does that child have a genuine understanding of university-level mathematics, or was she just taught a few tricks? Why didn’t she study A before B? What about C? If she’s in a gifted program, is her accomplishment truly her own, or just an artifact of having that kind of training? If she’s not in a gifted program, is that because she wasn’t good enough to qualify? Why does she have a recommendation from this person and not from that one? Will she have a capacity for research or creative work, or is she just good at solving puzzles? There are concerns: is there something wrong with her? Is she autistic, or at least somewhere on the spectrum? Does all that mathematics come at the expense of her physical or social development? Does she have friends? Does she have a childhood?

Girls are not the exclusive subject of such scrutiny. I have personally witnessed similar conversations with regard to male prodigies (spoiler: the people in question turned out fine). However, based on my own experience and on my observations as a professor and educator, I would say that boys generally have a much wider interval of “acceptable giftedness” available to them. We are quicker to recognize talent in boys, just like it’s easier for us to hear the same points when they are made by men or see promise in the same CV when it has a male name attached to it. This is typical:

My 9th-grade geometry teacher called a boy to the front of the class and praised him for being the only person to correctly answer the bonus question at the end of that week’s test. I raised my hand (very out of character for me, but that’s another story…) to remind him that I had also answered it correctly, but he responded by saying he hadn’t forgotten, he just hadn’t felt it was worth mentioning because GIRLS CAN’T DO MATH!

I searched for female names in this article on a decades-long “Study of Mathematically Precocious Youth,” initiated by Julian Stanley at the Johns Hopkins University in the early 1970s, and its various offshoots. Only one woman (Stefani Germanotta, aka Lady Gaga, certainly one of the smartest people on the planet but not exactly a mathematician) is explicitly named as an alum of one such program. Two other women who might or might not have been in the program (“a protégé of Stanley’s” and “studied with Stanley,” respectively) are mentioned in the text. Both work as educators (no particular connection to STEM is mentioned), and both of their quotes are about Stanley. By contrast, we do get names of well known male mathematicians and tech entrepreneurs who were formerly identified as gifted students, as well as further names of a male physicist and male engineer who did not qualify for a different gifted program. The student in the anecdotal story opening the article is also male. This is just one article, no better or worse than many similar ones out there. When we look for mathematically gifted children, we do not see girls.

At the same time, boys can go much further than girls along the prodigy spectrum before we start asking that whether being that good is really good for them and whether they should perhaps be gently steered away from it. A boy may have to be seven or eight grades ahead of schedule before he faces such concerns; for a girl, two or three might suffice. There is more social pressure on her to be “normal” and more backlash if she tries to be too successful. There can be open hostility as well. The war on smart women does not wait for them to reach any particular age. Again, this does not only happen to girls. In one scene in “Gifted,” a boy gets tripped up by a classmate because his artwork was too good. Mary comes to his defence, violently, which should really get her in trouble but in the end she just has to promise that she won’t do it again. I submit that this is the wrong question to ask. The right question would be: what will she do when her classmates start tripping her up? Because that will happen. If a particularly good art project was too much for some of these kids, let’s see their response when they find out that Mary is attending university classes on the side.

For storytelling purposes, having the child prodigy be a girl instead of a boy can be an excellent dramatic choice if you follow up on it and engage with the implications. The stakes and contradictions are higher, the reactions more varied and extreme, disagreements more fundamental. If the local community’s response to Mary is not informed by sexism, then I want to know more about how that happened. There are dads who teach their daughters calculus. There are enclaves, often minority or immigrant, where girls are not discouraged from excellence in mathematics. There are exceptions to exceptions, and they have amazing stories to tell. Or, if you prefer, have Mary grow up with the Amazons on a secret island where everyone is doing kick-ass mathematics. I’ll suspend disbelief for the duration.

Instead, in a film planted firmly in the present-day USA complete with health insurance woes, featuring a major character who (it is suggested) never came to terms with having surrendered her ambitions to gendered expectations a few decades earlier, we are asked to believe that we have since become gender-blind and sexism no longer exists. We are also presented with a loving and sympathetic father figure who wants Mary to put aside those awful math textbooks, and a grandmother who encourages Mary’s passion for mathematics but, on closer inspection, turns out to be an inhumane monster. There is even a damsel in distress moment where Frank mounts a rescue operation to save his little girl.

The main conflict revolves around the question of whether Mary should receive some kind of gifted education such as being placed in a school for gifted kids. That is a legitimate cause for disagreement, and I honestly don’t think I could yay or nay it without knowing more about both Mary and the specific program under consideration. Gifted programs can provide education that’s more challenging, more interesting, and better tailored to the child’s individual needs. Surrounded by kids similar to herself, Mary would not have to conceal her abilities and temper her achievements in order to fit in, as too many girls do. Scholarships and early college access are not just CV bullet points – they also offer flexibility and independence that can be quite useful when, for example, one happens to have an abusive and controlling grandmother. On the other hand, American-style gifted programs can be extremely demanding in terms of sheer volume of the work required, with no time for leisure or independent pursuits. That can leave the students overwhelmed, frustrated and depressed. Some programs, dominated by kids from wealthy families, have a culture that not everyone might find welcoming. Certain types of gifted education require a supporting team: parents and family managing the child’s schedule, providing transportation to various classes and arranging the right types of extracurricular activities, school teachers making special arrangements for the kid’s tests and exams, private tutors filling in various gaps. Not all gifted kids have such teams available, and those who do might end up acquiring a somewhat skewed impression of their place in relation to the rest of the world.

But Frank rejects all suggestions of gifted programs for Mary straight out of hand, as if they were an absolute evil that must be avoided at all costs. Even when faced with the possibility of losing custody of the child altogether, he still does not relent, refusing for a long time to even discuss the options or negotiate alternatives that might be acceptable to all parties. This could be psychologically realistic for someone who has traumatic memories associated with gifted education, which Frank does. However, if we’re talking about psychological realism, then let’s not introduce Mary as a fully formed mathematical miracle who could have emerged from her mother’s womb computing integrals for all we know. The battle is fought on general principles taken to the extreme, but it can’t be resolved satisfactorily on those principles alone, with “gifted programs” as an abstract quality and Mary as a little black box in the middle of it. Sure, we get to know her to some extent. She’s an adorable little girl with a cat and an attitude. For prodigies, though, their giftedness is not just incidental to who they are otherwise, it’s a defining part of them. So is being, visibly and obviously, a work in progress. This does not mean that Mary should be a weirdo with no interest in anything but mathematics. It means that we would like to see something of how she learns those integrals and what drives her to do so.

That would be the film about math prodigies that I hope someone will make one day: one that respects, and is curious about, the learning process. Let’s see the nuts and bolts, the emotional turmoil, the breakthroughs and defeats, the unnerving manifestations of the trainee’s innate ability, the distinctions between what comes naturally and what must be studied and practiced regardless of talent. Additionally, while generally a controlling parent does not need a gifted child to be controlling – any child will do – there is a specific kind of troubled dynamics that can exist between a gifted but traumatized mother and her similarly, only more, gifted daughter. If these are things you’re interested in, skip “Gifted” and read N.K. Jemisin’s “The Obelisk Gate” instead. (You will have to start with “The Fifth Season” though, since “The Obelisk Gate” is not a stand-alone book.) I confirm from my own experience that she gets it just about right, and I would love to see a story similar in depth and scope to Jemisin’s mother and daughter thread where the protagonists are female mathematicians.

As it is, my favourite prodigy film is probably “Hilary and Jackie,” about the du Pré sisters at several different stages of their musical and family lives. Based on a book written by Hilary du Prė and her brother Piers, it’s messy, often painful, true to the complexity of the choices that prodigies and their families must make. Ebert wrote:

“Would you still love me if I couldn’t play?” Jacqueline asks her husband. “You wouldn’t be you if you didn’t play,” he replies, and that is the simple truth made clear by this film. We are what we do.

I think I’d still be me if I stopped being a professional mathematician, but mathematical thinking, understood more broadly, will always be an essential part of who I am. The impact of having been a prodigy wears off as time goes by. Some details get blurry. It no longer matters whether I knew logarithms when I was in fifth grade or only in eighth. Years gained through skipping grades can be easily lost later on, then gained and lost again. If there’s any part of it that has stayed with me and echoed through my research career, it would be the messy part that “Gifted” skips altogether. Trying out things before you are ready for them. Approaching them without a guide or a syllabus, just starting somewhere and digging in. Failing. Failing again. Cutting through the noise. Pushing through embarrassment and discouraging advice.

I still do that. I wouldn’t be me if I didn’t.