In a week of dismaying news, there was a ray of sunshine: a scientific breakthrough with the potential to change lives. Men and women’s brains have finally been proved, by actual scientists, in a massive study, to be completely different! This, you gathered, was the substance of a prominently reported new study that made the front page of the Times: “Men and women really do think differently, say scientists.”

In another paper, the headline specified how: “The sex divide: female empathy vs male logic”. Dr Varun Warrier, of the research team, was widely quoted, saying: “These sex differences in the typical population are very clear.”

Rarely, if ever, since social impact was added to official measurements of academic excellence, can a psychology study have enjoyed a reception as extensive, and thus far as warm, as this new contribution, from four Cambridge researchers, to the scholarly literature on sex difference. Perhaps discouragingly for their colleagues, it appears that the findings, rather than the field itself, account for the paper’s remarkable appeal. To date, no equivalent headlines – Men and women’s thinking can be surprisingly similar! – have welcomed contradictory work, such as Cordelia Fine’s, on the destructive fallacies of gendered minds.

Admittedly, the new study had its critics: Gina Rippon, professor of cognitive neuroimaging at Aston University, had reservations about its reliance on self-reporting (to a Channel 4 online questionnaire, in which subjects identified, or not, with statements such as “I am good at predicting how someone will feel”). Rippon noted that the respondents, aged between 16 and 89, would have had “plenty of time to have absorbed the gendered messages to which they will have been exposed”.

Elsewhere, the neuroscientist and author Dean Burnett pointed out, in a comprehensive demolition, that the study of sexed brain difference “doesn’t look at brains, at all”.

Broadly, however, the reported message remained, like the original research, supportive of pink/blue thinking on human behaviour and, incidentally, of the employment status quo. In fact, given the prominent and, for the most part, respectful coverage of this research, its cultural impact could surely go beyond news headlines and broadcasts, to the point of shaping thinking on fixed behavioural traits, even to influencing policymaking, or employment, especially if the study’s “very clear” sex differences can be aligned with covert sex discrimination. You can imagine, for instance, the utility of the Cambridge research at the BBC, where women have long been diagnosed as temperamentally unsuited for some journalistic work; yet more so in the City, where companies are currently defending themselves against findings of the Hampton-Alexander review. It has just revealed a decline, last year, in the number of women CEOs in the FTSE 350, from 15 to 12.

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A familiar excuse, when FTSE companies were asked why they didn’t appoint women, seems to have been the increasingly threadbare one of shortages: “All the ‘good’ women have already been snapped up.” We heard something similar from David Cameron, during his valiant struggle to find women of the calibre of Johnson, Gove, himself.

Now, however, the resourceful City, judicial, political, medical or tech misogynist can invoke the Proceedings of the National Academy of Sciences, publisher of the Cambridge paper, and accompanying media glosses such as this, in the Mail: “Cambridge academics tested 670,000 people and found men are typically better at analysis and problem-solving and better suited to rule-based jobs such as engineering.”

From an impact-measuring perspective, the close resemblance between these findings and amateur suspicions that deter or exclude women from “rule-based jobs” could make it difficult to establish how much inequality at work owes to new, evidence-based scholarship. Perhaps it’s the other way round?

Either way, some common ground probably accounts for the extraordinary media excitement about a study entitled “Testing the Empathizing–Systemizing theory of sex differences and the Extreme Male Brain theory of autism in half a million people”.

Hats off, too, to Cambridge University’s PRs, who seem correctly to have calculated that the words “largest ever study” were more likely to win this research an audience that is arguably, given its methodology, unmerited. That individual empathising-systematising differences can’t possibly be predicted, being the result (as the researchers say) of unknown interactions between genetic, hormonal and environmental factors, was also likely to inspire less interest than the university’s announcement of “psychological sex differences”.

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It must have been obvious, including to the researchers, that an unobtrusive warning that their generalisations should not encourage stereotyping is unlikely to deter people seeking confirmation, say, that psychological differences make women scientists more likely to cry, or less likely, as an Italian professor has claimed, to deserve jobs in physics. Whatever it does or does not show about sex difference, the new research has already demonstrated how little it takes for James Damore’s supporters on social media to claim vindication for the Google martyr who was sacked after arguing that women’s brains made them less suited to tech, like him, than to “jobs in social or artistic areas”.

Which statement do you identify with? This, from the psychologist Cordelia Fine: “Neuroscientists in socially sensitive areas like gender should work under a burden of caution. Many studies are flawed, many are over-interpreted. But not many inspire in their authors and others the conclusion that innate differences in part lie behind our gender-stratified society.”

Or this amended version: “Neuroscientists in socially sensitive areas like gender, even if they understand that a methodologically unimpressive research paper could reinforce stereotypes that impair people’s life chances, should put its promotion first, regardless of the consequences.”

Whether or not your response to the above makes you more or less adept with flatpack furniture assembly, it could well indicate your suitability for research work at the University of Cambridge.

• Catherine Bennett is an Observer columnist