It’s an intuitive claim, but also a profound one. It asserts that the benefits of bilingualism extend well beyond the realm of language, and into skills that we use in every aspect of our lives. This view is now widespread, heralded by a large community of scientists, promoted in books and magazines, and pushed by advocacy organizations. Its proponents point to reams of studies showing benefits of bilingualism on executive function, in everyone from pre-schoolers to elderly adults.

But a growing number of psychologists say that this mountain of evidence is actually a house of cards, built upon flimsy foundations. According to Kenneth Paap, a psychologist at San Francisco State University and the most prominent of the critics, bilingual advantages in executive function “either do not exist or are restricted to very specific and undetermined circumstances.”

Paap started looking into bilingualism in 2009, having spent 30 years studying the psychology of language. He began by trying to replicate some seminal experiments, including a classic 2004 paper by Bialystok involving the Simon task. In that task, volunteers press two keys in response to colored objects on a screen—for example, right key for red objects, left for green. People react faster if the position of the keys and objects match (red object on right half of the screen) than if they don’t (red object on left). But Bialystok found that twenty Tamil-English bilinguals from India were faster and more accurate at these mismatched trials than twenty English-speaking monolinguals from Canada. They were better at suppressing the location of the objects and focusing on their color—a sign of superior executive function.

“It was a really exciting finding and one that I thought would be easy to study with my students,” says Paap. “But we just couldn't replicate any of the effects.” After years of struggling, he published his results in 2013: three studies, 280 local college students, four tests of mental control including the Simon task, and no sign of a bilingual advantage.“That broke the dam,” he says. “Others started submitting negative results and getting their articles published.”

Jon Andoni Duñabeitia, a cognitive neuroscientist at the Basque Center on Cognition, Brain, and Language, was one of them. In two large studies, involving 360 and 504 children respectively, he found no evidence that Basque kids, raised on Basque and Spanish at home and at school, had better mental control than monolingual Spanish children. “I am a multilingual researcher working in a multilingual society,” says Duñabeitia. “I'd be very happy to see an advantage for bilinguals! But science is what it is. We find no difference and we have replicated it several times, in older adults, kids, and young adults at university.”

Similar controversies have popped up throughout psychology, fueling talk of a “reproducibility crisis” in which scientists struggle to duplicate classic textbook results. In many of these cases, classic psychological phenomena that seem to be backed by years of supportive evidence, suddenly become fleeting and phantasmal. The causes are manifold. Journals are more likely to accept positive, attention-grabbing papers than negative, contradictory ones, which pushes scientists towards running small studies or tweaking experiments on the fly—practices that lead to flashy, publishable discoveries that may not actually be true.