In the late 1960s, a Hungarian teacher named László Polgár resolved to try an educational experiment.

The author of a brassy parenting book called Bring Up Genius!, he sought to prove that, as one of his kids later put it, “any healthy child—if taught early and intensively—can be brought up to be exceptionally successful in any field.” He married a fellow teacher who shared his views, and together they had three daughters. When the eldest took an interest in his chessboard as a toddler, László realized the game—with its objective measures of success—would make an ideal test of his method.

He could not have set the stakes higher. Top-level chess had long been considered a domain in which women were mentally incapable of competing. But László and Klara Polgár scorned the received wisdom. “Women are able,” László insisted, “to achieve results similar, in fields of intellectual activities, to [those] of men. Chess is a form of intellectual activity…. Accordingly, we reject any kind of discrimination in this respect.”

With the help of elite coaches, the Polgárs drilled their daughters in the art of chess. All three turned into prodigies.

In 1991 Zsuzsa (Susan) became the first female grandmaster in the history of the sport. The second child, Zsófia (Sofia), became an International Master. And the third, Judit, topped them all. At age 15 she became the youngest player ever to reach grandmaster status. As an adult she racked up victories against the likes of Boris Spassky, Magnus Carlsen, and Garry Kasparov, who had once declared that “women by their nature are not exceptional chess players.” At her peak she was ranked No. 8 in the world.

Was there a genetic component at work? Possibly—but Klara was a nonplayer, László an average talent whom Judit could beat by age five. Is Judit the rare successful product of an experiment at which other families fail in obscurity? Maybe. But how many such families could there be? Few Western parents coach their toddler daughters relentlessly in anything, let alone chess. Even fewer declare, and make good on, their intent to raise a certain type of genius.

If the Polgárs’ experiment had been even a little less successful—if all three daughters had “only” become masters, or if one had become an obscure grandmaster while the others lost interest—you might call it a fluke, or evidence of a ceiling for female chess players. But Judit became one of the top ten players on the planet. She beat the best human player of all time. She became, for a brief spell, the greatest chess prodigy in human history. She blitzed to the forefront of a game at which women were considered hopeless, exactly as her parents had envisioned before she started playing. Most of us can only dream of being so right about something.

The Polgárs’ story is more than inspiring: it’s the most remarkable “nature vs. nurture” anecdote I know.

And while it is only an anecdote—no conclusive proof of anything—it drives some recent theories of group cognitive inequality into a tight corner. Study its implications and you start to smell checkmate.

The theories in question are now linked forever in the public mind with Larry Summers. Summers’ suggestion, in 2005, that gaps in “intrinsic aptitude” might explain the gender gap in STEM fields (science, technology, engineering, math) plunged him in deepening controversy until his resignation as president of Harvard the following year. Defenders cast him as a martyr to ivory-tower pieties; critics charged that his speculation was, at the very least, obnoxious in the absence of hard evidence.

Chess isn’t an academic discipline, but like STEM fields its gender imbalance is often attributed to differences in analytical, spatial, and calculation skills—in short, intellectual disparities. In the same year as the Summers gaffe, researchers Paul Irwing and Richard Lynn published a paper concluding that “different proportions of men and women with high IQs…may go some way to explain the greater numbers of men achieving distinctions of various kinds for which a high IQ is required, such as chess Grandmasters, Fields medalists for mathematics, Nobel prize winners, and the like.”

Immediately we notice that these achievements “of various kinds” don’t seem to extend to the humanities (Nobel-winning authors aside). Is high IQ less important in these “soft” fields, where women have successfully struggled for greater parity? Could it be that fields in which men still dominate are reflexively defined as more cerebral?

In any case, these hard rationalists may have overlooked a more logical reason for the gap. In a 2009 paper for the Royal Society’s biology journal—provocatively titled “Why are (the best) women so good at chess?”—Merim Bilalić and his co-authors advance “a simple statistical explanation” for modern chess demographics:

…the extreme values in a large sample are likely to be greater than those in a small one. Although the performance of the 100 best German male chess players is better than that of the 100 best German women, we show that 96 per cent of the observed difference would be expected given the much greater number of men who play chess.

Bilalić immediately notes that this same explanation “may also be the main reason why women are under-represented at the top end” of science. But since “greatness” in science is pretty subjective—in fact, often distorted by systemic prejudice (were Watson and Crick greater than Rosalind Franklin?)—he focuses on chess, whose scrupulous ratings system permits fair comparisons.

In naming participation rates as the culprit, he anticipates a rebuttal: “Women may be inferior in the intellectual abilities that are important for successful chess playing. This innate disadvantage may lead women to give up on chess in greater numbers than more successful men.” But the numbers don’t bear it out: Bilalić points to a 2006 study showing similar chess dropout rates for boys and girls. Instead the gender gap seems to start “in the early stages” before tournament play.

Bilalić’s conclusions are backed by a similar 1996 study in Psychological Science, which attributes both “Russian and Male Dominance in Chess” to unequal participation. Even those girls who participate in competitive chess are often barred from playing against men, as Judit Polgár herself recently lamented to The Australian. Polgár blames [the gap on] a worldwide reluctance to let girls compete against boys. “The problem is in chess that all the girls should be not competing between themselves—they should always compete in a higher level so they can improve faster,” she said.

Have the game’s male gatekeepers confused cause and effect here—or been “reluctant” to see it clearly? According to Polgár, women aren’t rare in high-level chess because they lack the necessary skills; they lack those skills because they’re rarely allowed to compete at high levels. ForBilalić the major culprit is sheer non-participation, starting at a young age despite women’s initial parity in talent.

Bilalić believes “there is little left for biological or cultural explanations to account for” beyond this statistical underrepresentation. But what about cultural explanations for the underrepresentation? Might more attention and resources be lavished on young boys who take an interest in chess? Might girls be deterred by condescension from figures like Kasparov? Or the late Bobby Fischer, who claimed: “They’re all weak, all women. They’re stupid compared to men”? Or Judit’s own coach, who once told her she was “an exception, not a girl”?

Old-fashioned coaches aren’t alone in imagining geniuses as superhuman “exceptions,” blessed with ethereal gifts. Yet more and more research indicates that all mastery, all brilliance, is to a startling extent the product of gritty persistence.

In a 2006 Scientific American article on “The Expert Mind,” Philip E. Ross wrote: [Herbert A.] Simon coined a psychological law of his own…which states that it takes approximately a decade of heavy labor to master any field. Even child prodigies, such as Gauss in mathematics, Mozart in music, and Bobby Fischer in chess, must have made an equivalent effort, perhaps by studying earlier and working harder than others. According to this view, the proliferation of chess prodigies in recent years merely reflects the advent of computer-based training methods…

That the proliferation of chess prodigies started a few years after the Polgárs’ rise makes you wonder if it reflects their example too. Indeed, Ross cites Judit as the world’s first proof that “grandmasters can be reared.” He acknowledges that such findings challenge our conception of specialness:

Surely, [skeptics] will say, it takes more to get to Carnegie Hall than practice, practice, practice. Yet this belief in the importance of innate talent, strongest perhaps among the experts and their trainers, is strangely lacking in hard evidence to substantiate it. In 2002 [Fernand] Gobet conducted a study of British chess players ranging from amateurs to grandmasters and found no connection at all between their playing strengths and their visual-spatial abilities, as measured by shape-memory tests.

“Visual-spatial abilities” also come up a lot in discussions of the STEM gap. Men typically test better on them than women, and unlike chess, some STEM fields (chemistry, engineering) undeniably require them. Michigan Tech’s Sheryl Sorby has shown, however, that focused training in spatial tasks dramatically improves test scores, and that women who receive it not only catch up but are more likely to remain in STEM fields. So nature’s claims shrink further: a disparity once thought to separate grandmasters from wannabes, male scientists from struggling female peers, turns out to be eminently surmountable by nurture where it matters at all.

Why do women’s scores lag at the outset? One predictor of initial success, Sorby has found, is “play as children with construction toys such as Legos, Lincoln Logs, and Erector Sets.” Any progressive parent will see where I’m going here; we’ve grown more sensitive to the dangers of such pigeonholing, but it’s hardly been flushed out of the culture. A 2010 American Association of University Women report on the STEM gap (pdf) quotes Joshua Aronson, a path-breaking researcher on gender stereotyping:

Girls do every bit as well in their graded work [as] boys [do], but girls lose confidence as they advance through the grades….One reason for this loss of confidence is the stereotyping that kids are exposed to—in school and the media and even in the home—that portrays boys as more innately gifted [in math]. Without denying the fact that boys may have some biological advantage, I think that psychology plays a big role here.

Again we see the almost Freudian importance of early life, early lessons, including lessons others may not realize they’re teaching. But the vast gulf Freud imagined between male and female minds—the Victorian phrenologists’ gloating over gender and skull size—the old saw that men are rational by nature and women emotional: what’s left of them? Modest, provisional assertions about mental rotation tasks and women clustering closer to the center of the bell curve.

Let’s be clear about what this isn’t. It isn’t a claim about overall intelligence. Nor is it a justification for tolerating discrimination between two people of equal ability or accomplishment. Nor is it a concession that genetic handicaps can’t be overcome. Nor is it a statement that girls are inferior at math and science: It doesn’t dictate the limits of any individual, and it doesn’t entail that men are on average better than women at math or science. It’s a claim that the distribution of male scores is more spread out than the distribution of female scores—a greater percentage at both the bottom and the top.

That’s William Saletan defending Larry Summers in 2005. True, the jury is still out on this claim, along with the Darwinian explanations posited in support of it. (Nature might have selected against risky genetic “extremes” in women, whose successful reproduction mattered more to early tribes’ survival—then again, culture, too, often lumps women together.) Yet the broader trend leaves you skeptical. In one century the domain of purported male intellectual superiority has narrowed from “all academic disciplines” to “the sciences” to “the hard sciences” to “a few mental abilities that may favor a few men in the hard sciences.” (And certain board games.)

Given this pattern, it’s unclear why even the admirable Aronson seems reluctant to discount “some biological advantage.” At what point does the burden of proof—and clarification—shift onto those proposing “some” such factor? When does simple intellectual equality become the working hypothesis?

The footage of Kasparov’s loss to Polgár is striking. He stares glumly at the board till the inevitable moment. He turns his head almost completely away, shakes her hand for a millisecond, and leaves the table. He never looks her in the eye.

Later the great champion recovered a measure of grace. In his book How Life Imitates Chess, he acknowledged that “the Polgárs showed that there are no inherent limitations to their aptitude—an idea that many male players refused to accept until they had unceremoniously been crushed” by one of them.

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Now that all chess players are crushed by the raw calculating power of computers, it’s worth glancing back at the richly human history of the game. Pastime of kings and park-bench hustlers, its cultural role has shape-shifted through the ages. In “False Play: Shakespeare and Chess,” William Poole notes that “chess was the medieval and Renaissance symbol of courtly, aristocratic entertainment, even of sexual equality.” Surveying “The Politics of Chess in Renaissance Italy,” Patricia Simons finds allegories of the gameboard as “a site of potential temptation, overarching competitiveness or lascivious meetings”; of “martial action,” “feminine lust,” or fraught encounters between the sexes:

The symbolism of a competitive battle of wits and assertion of mastery could lend itself to gender politics. So several Italian depictions of chess contrast male and female players at the same board, continuing the tradition of certain medieval romances.

Then there’s that most famous literary chess match, the one in The Tempest. Raised on a desert island, Miranda delights in squaring off against her new love Ferdinand, the first young man she’s ever met. As more of his fascinating kind approach, she exclaims: “…O brave new world,/That has such people in’t!” To which her father retorts: “‘Tis new to thee.”

Marveling over the Polgárs, a writer risks sounding like wide-eyed Miranda. When I first came across their story it bowled me over. I’d never lent much credence to the Larry Summers hypothesis, but these women seemed to have finished it off and smacked the gameclock. That impression turned out to be bolstered by a rising stack of research, some of it two decades old—but, ‘twas new to me.

None of this makes their achievement less thrilling—less ringing a testament to human potential. Of course nature still counts for something; Judit stood out even among her sisters. It’s just that the plasticity, the amazing educability of the mind turns out to be so common a part of our human natures. So humbling, too: because it’s not an exclusive privilege, and because it can be squandered. The superstitions by which we impute superior talent to this or that group, credit this divine spark or that sacred puff of wind, so often seem defensive reactions to the circumstances of our own early training.

This summer Judit Polgár announced her retirement, ceding the title of No. 1 female player to Hou Yifan, who became a grandmaster at 14. For the first time a woman has just won the Fields medal in mathematics; for the first time a woman reigns as the world’s most powerful economist. Anecdotes, scattered data points—but they’re plotting something, shaping a hazy scene…

One half of the species plays chess against the other and, at long last, looks up. Meets the other’s eyes. Feels a boyish anxiety, but also a sense of relief. Any bystander can see—without believing in brave new worlds or happily-ever-afters—that the match is remarkably even; the competition is only a diversion; the rivals are in league.