When they finally published their study, in a May 2008 issue of Proceedings of the National Academy of Sciences, the results were striking. Before training, participants were able to correctly answer between 9 and 10 of the matrix questions. Afterward, the 34 young adults who participated in dual N-back training for 12 weeks correctly answered approximately one extra matrix item, while those who trained for 17 weeks were able to answer about three more correctly. After 19 weeks, the improvement was 4.4 additional matrix questions.

“It’s not just a little bit higher,” Jaeggi says. “It’s a large effect.”

The study did have its shortcomings. “We used just one reasoning task to measure their performance,” she says. “We showed improvements in this one fluid-reasoning task, which is usually highly correlated with other measures as well.” Whether the improved scores on the Raven’s would translate into school grades, job performance and real-world gains remained to be seen. Even so, accompanying the paper’s publication in Proceedings was a commentary titled, “Increasing Fluid Intelligence Is Possible After All,” in which the senior psychologist Robert J. Sternberg (now provost at Oklahoma State University) called Jaeggi’s and Buschkuehl’s research “pioneering.” The study, he wrote, “seems, in some measure, to resolve the debate over whether fluid intelligence is, in at least some meaningful measure, trainable.”

For some, the debate is far from settled. Randall Engle, a leading intelligence researcher at the Georgia Tech School of Psychology, views the proposition that I.Q. can be increased through training with a skepticism verging on disdain. “May I remind you of ‘cold fusion’?” he says, referring to the infamous claim, long since discredited, that nuclear fusion could be achieved at room temperature in a desktop device. “People were like, ‘Oh, my God, we’ve solved our energy crisis.’ People were rushing to throw money at that science. Well, not so fast. The military is now preparing to spend millions trying to make soldiers smarter, based on working-memory training. What that one 2008 paper did was to send hundreds of people off on a wild-goose chase, in my opinion.

“Fluid intelligence is not culturally derived,” he continues. “It is almost certainly the biologically driven part of intelligence. We have a real good idea of the parts of the brain that are important for it. The prefrontal cortex is especially important for the control of attention. Do I think you can change fluid intelligence? No, I don’t think you can. There have been hundreds of other attempts to increase intelligence over the years, with little or no — just no — success.”

At a meeting of cognitive scientists last August, and again in November, Engle presented a withering critique of Jaeggi and her colleagues’ 2008 paper. He pointed to a variety of methodological weaknesses (many of which have been addressed in subsequent papers by Jaeggi and others) and then presented the results from his own attempt to replicate the study, which found no effect whatsoever. (Those results have yet to be published.)

The most prominent takedown of I.Q. training came in June 2010, when the neuroscientist Adrian Owen published the results of an experiment conducted in coordination with the BBC television show “Bang Goes the Theory.” After inviting British viewers to participate, Owen recruited 11,430 of them to take a battery of I.Q. tests before and after a six-week online program designed to replicate commercially available “brain building” software. (The N-back was not among the tasks offered.) “Although improvements were observed in every one of the cognitive tasks that were trained,” he concluded in the journal Nature, “no evidence was found for transfer effects to untrained tasks, even when those tasks were cognitively closely related.”

But even Owen, reached by telephone, told me that he respects Jaeggi’s studies and looks forward to seeing others like it. If before Jaeggi’s study, scientists’ attempts to raise I.Q. were largely unsuccessful, other lines of evidence have long supported the view that intelligence is far from immutable. While studies of twins suggest that intelligence has a fixed genetic component, at least 20 to 50 percent of the variation in I.Q. is due to other factors, whether social, school or family-based. Even more telling, average I.Q.’s have been rising steadily for a century as access to schooling and technology expands, a phenomenon known as the Flynn Effect. As Jaeggi and others see it, the genetic component of intelligence is undeniable, but it functions less like the genes that control for eye color and more like the complex of interacting genes that affect weight and height (both of which have also been rising, on average, for decades). “We know that height is heavily genetically determined,” Jonides told me during our meeting at the University of Michigan. “But we also know there are powerful environmental influences on height, like nutrition. So the fact that intelligence is partly heritable doesn’t mean you can’t modify it.”