After Quillette published an essay by evolutionary biologist Carole Hooven titled, “Why Do Men Dominate Chess?,” a number of friends asked me if her essay explained a similar phenomenon in my own field of mathematics. After all, aren’t many of the traits that Hooven identified as crucial to excellence in chess—innate spatial ability, competitiveness, obsessiveness—similarly crucial for excellence in mathematics? And don’t men dominate mathematics for some of the same reasons?

Why Do Men Dominate Chess?

FIDE’s new policy governing who can compete in women’s categories highlights the persistent sex imbalance at the game’s elite levels.

QuilletteCarole Hooven

Hooven states that there does not appear to be much dispute about the size or persistence of sex gaps in chess, and she wonders if biology might play a significant role in men’s domination of the game. Her study was prompted by a ruling from FIDE, the International Chess Federation in Switzerland, stipulating that transgender women may not compete in official FIDE women-only chess tournaments, which often carry substantial financial rewards and recognition. That suggests that men may have some biological advantage in chess. Is this also the case in mathematics?

To quantify what she means by dominance, Hooven reports that “the fair sex accounts for only about two percent of the world’s chess Grandmasters.” But mathematics does not have Grandmasters, and unlike its close scientific field of physics, there are no Nobel prizes in mathematics. Common criteria for distinction in mathematics, such as the number of PhDs or professorships an institution awards, are decided by committees and these are often quite political. On the other hand, there are some clear objective measures in mathematics analogous to chess’s world championships.

The statistics for the very highest levels of mathematics competitions—in age groups ranging from middle school MathCounts to the university-level Putnam Mathematical Competition and the annual International Mathematical Olympiad—suggest that sex statistics in mathematics closely resemble the chess statistics Hooven quoted in her essay. For example, about 95 percent (not all sexes were revealed) of the top-scoring 100 participants in the 2023 International Mathematical Olympiad were male.

Unlike chess, these three competitions are all age-restricted. But mathematics has two additional levels of distinction above world championships and Olympiads, and both are open to all comers. The first is the set of seven Millennium Prize Problems announced in 2000, the solution to each of which carries a prize of a million US dollars. A quarter-century later, only one of these, the Poincaré Conjecture, has been solved, by unemployed Russian mathematician Grigori Perelman, who turned down both the million dollar prize and a Fields Medal.

The very highest level of mathematics challenges and accomplishments, which carry no monetary award at all, is solving one of the famous historical mathematics questions that date back to the ancient Greeks. My personal favourite still-unsolved problem is Goldbach’s 1742 gem: Is every even integer greater than two the sum of two prime numbers? Yes or no?

Solving one of these problems brings the highest recognition among mathematicians, and sometimes even the general public. When Princeton mathematician Andrew Wiles was able to solve Fermat’s 1637 conjecture in 1995 after working on it for nearly eight years, mostly in isolation and in secret, his discovery instantly made international news. The sex statistics for solving these conjectures are as persistent and one-sided as those for chess. For instance, of the roughly two-dozen famous conjectures that have finally been cracked by lone mathematicians in the past fifty years, every one has been solved by a man.

Men’s domination at the highest levels of mathematics is much more contentious than their dominance in championship chess for several reasons. For starters, almost every human being on the planet, whether good at mathematics or not, is forced to learn and use at least some basic arithmetic and algebraic skills in daily life.

Another important difference between chess and mathematics is that mathematics is often both fascinating and useful to the general population. For example, an article by applied mathematician Herman Chernoff titled, “How to Beat the Massachusetts Numbers Game” made instant news, and Benford’s Law is employed internationally to detect financial and voting fraud as well as earthquakes. There are huge numbers of excellent careers at all levels in mathematics—teachers from grade school to graduate school, financial analysts, data scientists, sports statisticians, you name it. But only a handful of Grandmasters make a full-time living playing chess, and no one but dedicated chess aficionados cares about new opening or end-game chess strategies.

Unlike Olympic sports, but like chess, the International Mathematical Olympiad has both an open category that anyone may enter and separate competitions open only to girls or women. The annual open International Mathematical Olympiad is augmented by both a European Girls Mathematical Olympiad and a Chinese Girls Mathematical Olympiad. Although American girls’ teams have won medals, for reasons unexplained there are neither American nor International Girls Mathematical Olympiads at the present time. The renowned Putnam Mathematical Competition is also open to everyone, but instead of an additional women-only division, it has a special award for the highest-scoring female.

Since some of the women-only mathematics prizes also come with high perks—the Birman, Michler, and Street women-only mathematics awards, for example, each award US$50,000—the same question may soon arise in mathematics. Should transgender women be barred from female-only mathematics competitions and awards? Does biology play an important role, not only in tournament-level chess as Hooven suggests, but also at the highest levels of mathematical achievement?

The Greater Male Variability Hypothesis and Its Critics

In making the case for the role biology may play in championship chess, Hooven’s Quillette article did contain one significant error—she dismissed greater male variability (GMV) as a factor. This error does not affect her other arguments, and GMV may in fact provide strong support for why men appear to dominate the upper tiers of both chess and mathematics. Her error, as I will explain below, is a version of a fundamental logical error that continues to plague GMV-related research today.

The basic tenet of GMV, which dates back to Charles Darwin’s observation in his 1871 book The Descent of Man, is that throughout the animal kingdom, males generally tend to be more variable than females of the same species. In the highly controversial field of human cognition, for example, GMV has often been interpreted to mean that there are more idiots and more geniuses among men than among women.

Darwin’s questions about sex differences in variability continue to challenge science—over 350 scientific articles on the subject have been published since 2020, and GMV is generally accepted in many contexts. For example, using three different measures for differences in variability (Levene’s test, the variance ratio test, and the distances between cumulative distribution functions), Lehre et al concluded: