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From the book "The future is faster than you think" by Peter Diamandis, Steven Kotler:

“Consider the nine-dot problem, a classic test of creative problem-solving. Connect nine dots with four lines in ten minutes without lifting your pencil from the paper. Under normal circumstances, fewer than 5 percent of the population can pull this off. In a study run at the University of Sydney in Australia, none of their test subjects did. But then the researchers took a second group of subjects, and used transcranial direct stimulation to artificially mimic many of the changes produced during flow. What happened? Forty percent solved the problem—a record result.”

What is the current scientific consensus on this question?

This appears to be the study mentioned:
Brain stimulation enables the solution of an inherently difficult problem
https://www.sciencedirect.com/science/article/abs/pii/S0304394012003618

An APA reference to the study was requested.
Here is one such reference:
Using transcranial direct current stimulation to enhance creative cognition: Interactions between task, polarity, and stimulation site.
https://psycnet.apa.org/record/2017-24133-001

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There is no consensus on this question. This technique is relatively new, and has not been widely used so far. I know of one paper (below) that used this technique alongside intra-cortical recordings and do report convincing effects on LFPs (the overall activity of a local area) and behavior of non-human primates, but not on individual neurons. So this technique does have the potential to modulate brain activity on behaving humans.

For the paper you cite specifically, I do not know whether it is true or not. But solving the 9-dots problem is a hard and unspecified problem that presumably involves the participation of millions of neurons all over the brain. That you could improve performance so much by applying such a simplistic pattern of stimulation is more than highly dubious (in my opinion even laughable). It may be true, but if you asked me to bet I would feel very comfortable betting a large sum of money that such a result would not be replicated in a rigorous, large-scale, double-blind study.

As for consensus, you'll find multiple meta-analyses and reviews (example below) arguing that tDCS has no effect whatsoever on behavior. It doesn't mean there aren't studies reporting real effects in the mix, but the vast majority of studies I have seen so far were very dubious.

Krause, M. R., Zanos, T. P., Csorba, B. A., Pilly, P. K., Choe, J., Phillips, M. E., ... & Pack, C. C. (2017). Transcranial direct current stimulation facilitates associative learning and alters functional connectivity in the primate brain. Current Biology, 27(20), 3086-3096.

Horvath, J. C., Forte, J. D., & Carter, O. (2015). Quantitative review finds no evidence of cognitive effects in healthy populations from single-session transcranial direct current stimulation (tDCS). Brain stimulation, 8(3), 535-550.

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  • $\begingroup$ I may be willing to take you up on that bet. $\endgroup$
    – Arnon Weinberg
    May 9, 2020 at 7:25
  • $\begingroup$ Interesting. I have colleagues I respect who use this technique and report effects on low-level decision-making or memory tasks. The paper from Pack's lab was important but confusing, as they do not find effects on neuronal activity, only LFPs. Overall I wouldn't dismiss the technique out of hand. But I stick to my opinion whether it is likely to help you solve this 9-dots problem (it's not). $\endgroup$
    – user17122
    May 9, 2020 at 19:53
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Short answer: Most literature reviews and meta-analyses on cognitive enhancement from tDCS have found some promising effects, but it is too early to tell which specific effects will replicate.

... there is mixed evidence about whether tDCS is useful for cognitive enhancement in healthy people. Several reviews have found evidence of small yet significant cognitive improvements. Other reviews found no evidence at all ...

For examples of at least partially favourable reviews, covering many hundreds of studies, see Brunoni & Vanderhasselt (2014), Coffman, Clark & Parasuraman (2014), Price et al (2015), Dedoncker et al (2016) and Dedoncker et al (2016), Hill, Fitzgerald & Hoy (2016), Mancuso et al (2016), Summers, Kang & Cauraugh (2016), Hashemirad et al (2016), Weinberger, Green & Chrysikou (2017), Martins et al (2017), Katsoulaki, Kastrinis & Tsekoura (2017), Strobach & Antonenko (2017), Schroeder et al (2017), Ali, Mansoury, & Samaneh (2017), Schroeder & Plewnia (2017), Reteig et al (2017), Sellaro, Nitsche & Colzato (2017), Lucchiari, Sala & Vanutelli (2018), Huo et al (2019), Mayer et al (2020), and Wikipedia.

Stimulation protocols:

One notable exception is Horvath, Forte & Carter (2015), which found no evidence of cognitive enhancement from tDCS. Aside from the criticisms that this review has received (see here, here, and here), it did serve to highlight certain issues within this field. A few more recent reviews concur: eg, Barti et al (2020), Galli et al (2019).

Reasons for the mixed results found in some reviews may be that many studies are under-powered (see also Medina & Cason (2017)), or not long enough (see also Westwood & Romani (2017)).

More importantly however, tDCS interventions are still in an exploratory phase, and protocols are not yet established and consistent across studies. There is variability in stimulation location, polarity, intensity, definition, and arrangements. Thus, studies reporting null results do not necessarily indicate ineffectiveness - rather, they may just be setting boundaries on effective protocols. Time will tell.

This issue is further exacerbated by the potential specificity of protocol to task and possibly even to individuals. Although the likelihood of 20 years of research involving numerous experiments by many independent labs being found entirely spurious is fairly low, it is too early to tell which findings will ultimately pan out. As many of the literature reviews conclude: More replication is desperately needed.

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