The idea that success in STEM fields such as engineering, math, and physics requires “genius” is one of the factors identified as an obstacle to increasing the numbers of women in those fields.

lisa piccirillo head shot
Lisa Piccirillo, Ph.D., assistant professor of mathematics at the
Massachusetts Institute of Technology
Photo Credit: MIT News Office

The belief that brilliance, rather than hard work, is the key to success in these fields makes it difficult for women to rise to positions of leadership (Hu 2016). Researchers have found that women are better represented in certain STEM fields than others (e.g., molecular biology vs. physics). They found that these differences are best explained by the belief that innate talent is the key to success in those fields, rather than by the time demands required, differing levels of achievement, or whether the field requires systematizing or empathetic thinking (Leslie et al. 2016). The idea that innovative ideas are the result of “light-bulb” moments, rather than the careful nurturing of the “seed” of the idea, also has been found to favor the view that men, rather than women, possess the “genius” required to be successful in STEM fields (Elmore and Luna-Lucero 2017).

Mathematics is one of the fields in which genius is seen as an important element in success and in which women continue to be significantly underrepresented. The gender gap in math has been static for a number of years, with women earning fewer than 30% of mathematics doctoral degrees in 2018, although that same year, women earned 52% of all doctoral degrees (American Physical Society 2020). It is, therefore, significant that a young female mathematician who made a remarkable breakthrough in the field of mathematical topography challenges the view that breakthroughs like hers require genius.

Lisa Piccirillo, Ph.D., now an assistant professor of mathematics at the Massachusetts Institute of Technology, solved a vexing problem in knot theory in 2018 while still a graduate student. The so-called “Conway knot problem” involved the question of whether one of the many knots with 12 or fewer crossings possessed the quality known as “slice” (Klarreich 2020). The problem is a significant one for four-dimensional topology, involving thinking about three-dimensional spheres that can be viewed as the skin of a four-dimensional sphere.

This is the kind of problem that tends to be seen as the territory of geniuses — as one journalistic account of Dr. Piccirillo’s discovery put it, “Don’t worry if you are unable to conjure such a higher-dimension image for yourself. There are only a couple hundred specialists doing this in the world, and not even all of them can” (Wolfson 2020). This was the only such knot for which the question of sliceness had not been determined — the puzzle remained unresolved for more than 50 years.

She is eager to put an end to the myth of the math prodigy. Her view is that most good mathematicians aren’t prodigies and don’t have the stereotypical “child genius” background so often associated with them.

Dr. Piccirillo learned of the problem at a conference she attended and quickly saw a possible way to solve it. This involved using techniques she was using in another field of topology, rather than those that had been used for decades to tackle it. Within one week, largely in her spare time, she had determined that the knot was not slice. She shared her discovery with a professor in her home department at The University of Texas, who, after being initially skeptical, became extremely excited about her discovery. Dr. Piccirillo’s paper on the solution was published in a prestigious math journal soon after; the perception that she was a bit of a genius, a “hotshot” (Wolfson 2020), began to take hold.

Dr. Piccirillo herself rejects this perception. In her account of her discovery, she says that she didn’t work on the problem during regular work hours because “I didn’t consider it to be real math. I thought it was, like, my homework” (Wolfson 2020). Her background doesn’t involve the stereotypical math camps and prodigy-like early achievements associated with brilliant mathematicians. Instead, she was a strong math student, who benefited from having a mother who taught middle-school math, a female mentor who helped groom her during her undergraduate years at Boston College, and from the support of a female-friendly graduate math program at The University of Texas.

She is eager to put an end to the myth of the math prodigy. Her view is that most good mathematicians aren’t prodigies and don’t have the stereotypical “child genius” background so often associated with them. She urges the profession to avoid speakers who try to impress audiences with their brilliance and to work to become more welcoming and inclusive. Thus, a mathematician who could easily have become the poster child for the reality of genius instead asks mathematics to reject genius as a myth that excludes many capable people from the field.


American Physical Society (2020). Doctoral Degrees Earned by Women, by Major.

Elmore, K.C. and Luna-Lucero, M. (2017). Light Bulbs or Seeds? How Metaphors for Ideas Influence Judgments About Genius. Social Psychological and Personality Science 8(2): 200–208.

Hu, J.C. (2016). Why Are There So Few Women Mathematicians? The Atlantic, Nov. 4, 2016.

Klarreich, E. (2020). Graduate Student Solves Decades-Old Conway Knot Problem. Quanta Magazine, May 19, 2020.

Leslie, S.J. et al. (2016). Expectations of Brilliance Underlie Gender Distributions Across Academic Disciplines. Science 347(6219): 262–265.

Wolfson, J. (2020). A Math Problem Stumped Experts for 50 Years. This Grad Student from Maine Solved It in Days. MSN News, Aug. 20, 2020.

To learn more about Lisa Piccirillo’s work, please see the articles Young Topologist Solves Ages-Old Knotty Problem, from the Conference 2020 issue of SWE Magazine; and Brilliance: An Equal Opportunity Trait, a digital exclusive story from the Winter 2021 issue. (