The successful development of numerical cognition—one of the most advanced cognitive abilities that humans possess—is crucial.

Numerical and arithmetic abilities are highly related to career options, overall living standards, and are equally important for life success as literacy ^[1][2][1,2]. Numerical cognition is becoming progressively relevant, with increasing focus on quantitative aptitude in occupational settings, and in the well-established pervasiveness of technology.

On the other hand, atypical development of numerical cognition, such as dyscalculia, may increase the onset of neuropsychiatric symptoms, both internalizing and externalizing [3], especially when untreated. Interestingly, even when people do not present specific numerical cognition impairments, they may have everyday life problems in regard to manipulating numbers concurrent with specific anxiety symptoms—best known as math anxiety [4]. Math anxiety is an irrational emotional response, which includes tension, apprehension, or even dread, and it interferes with the ordinary manipulation of numbers and the solving of mathematical problems [4].

Numerical cognition impairment and its mental health-related consequences also imply significant public health expenditures—another variable not to be underestimated. For instance, in the United Kingdom, annual healthcare costs are estimated to equal nearly GBP 2.4 billion alone for numerical cognition difficulties [5].

With these premises, it is clear that an augmentation of numerical and arithmetic abilities could have a cascading effect on psychological levels as well as in the occupational and socioeconomic areas of people’s lives, supporting high qualities of life, well-being, and mental health. However, neurocognitive enhancement or interventional programs are still unrepresented, especially for individuals with dyscalculia.

In recent decades, there has been a significant amount of research into the investigation of neurocognitive architecture associated with numerical cognition ^[6][7][8][6,7,8]. With the identification of specific cerebral networks, so-called brain-directed interventions have been employed to enhance certain aspects of numerical cognition. Transcranial electrical stimulation (tES) is one of the brain-directed techniques that has garnered academic and public attention. tES is an umbrella term that encompasses a range of tools used to manipulate (directly and non-invasively) brain activity and, in turn, modulate the related cognitive process or behavior [9]. tES is considered a painless and safe, user-friendly, cost-effective intervention [9].

Despite plenty of studies investigating the effects of tES on numerical cognition, a few non-systematic reviews have been published thus far, with some evidence in favor of such brain-directed techniques ^[10][11][12][10,11,12]. Four years ago, a meta-analysis by Simonsmeier et al. [13] demonstrated that tES improved learning more than performance. In the stimulation of learning approach, participants first participated in a learning intervention, e.g., they practiced mental arithmetic, and they received brain stimulation before or during the learning phase. After the learning phase, participants completed a learning outcome measure (e.g., to see how strongly their mental arithmetic competences improved) without brain stimulation [13]. In the stimulation performance approach, participants were assessed on a psychological construct (e.g., mathematical competence) before or during brain stimulation [13]. The meta-analysis comprised a small portion of published findings on numerical cognition (i.e., 12 studies)—including studies on language. However, more than a handful of studies have been published since 2018 and a comprehensive and systematized synthesis of results, specifically in the numerical cognition domain, is, thus far, still missing. In parallel, the need for interventional or neuroenhancement programs is increasing, especially for those who do not benefit from a first-choice treatment option, such as children and adults with dyscalculia ^[14][15][14,15].

To date, available interventions for dyscalculia mainly consist of educational strategies grounded in the use of concrete material and informational feedback to the learner and/or programs aimed at improving children’s numerical understanding—with some evidence of efficacy ^[16][17][16,17]. However, standardized and integrated evidence-based interventions for dyscalculia are still not available.

To the best of our knowledge, this is the first systematic review that comprehensively evaluates the potential positive effects of tES techniques on numerical cognition. In particular, this researcha current systematic review would address the following research questions:

2. Current Insights

The originality and novelty of theour researchwork relies in its efforts to find a common thread and an integrative view to translate such results into clinical or neuroenhancement applications. In the following, thwe researchers will critically consider the results concerning non-symbolic and symbolic number processes and arithmetic processes. Afterwards, considerations of stimulation protocols for clinical translation as well as future directions and limitations will be discussed.

2.1. Does tES Consistently Enhance Numerical Cognition?

Despite plenty of published studies, the application of tES in numerical cognition is still a relatively novel field of research, considering that the oldest study was published in 2010. Its emergent phase justifies the heterogeneity found in the proposed methodology (i.e., stimulation protocols, tasks, or training employed) and the absence of clinical trials for neurodevelopmental disorders related to numerical cognition, such as dyscalculia. Overall, this resysearchtematic review reveals that most studies (20 out of 26) showed the effectiveness of tES in improving certain aspects of numerical cognition, whereas only a small number of studies documented tES null or worsened effects.

2.2. What Are the Numerical Cognition Aspects in Which tES Would Be More Effective? What tES Technique Would Be More Effective in Ameliorating Certain Numerical Cognition Aspects and under Which Stimulated Brain Regions?

Overall, the majority of studies reported beneficial tES effects on non-symbolic and symbolic number processes as well as arithmetic processes (respectively, 80% vs. 76%). TheOur findings suggest that tES can improve both aspects of numerical cognition, with a tendency to be more effective at affecting number processes. Given only a study that applied tACS on non-symbolic and symbolic number processes ^[18][75], thwe researchers discussed and compared results across tDCS and tRNS studies. All tRNS studies reported positive effects (two studies) while all but one tDCS studies produced beneficial findings. In particular, when comparing tDCS and tRNS over parietal regions, tES reported overall positive results on number processing (four tDCS studies ^{[19][20][21][22]}[70,71,73,76]; one HD-tDCS study ^[23][74]; two tRNS studies ^[24][25][77,78]). It should be noted that given the variabilities and heterogeneities in tES and task/training parameters, a direct comparison of studies was difficult, and results should be interpreted with caution. However, two tentative considerations may be relevant. First, the benefits of a bilateral parietal tDCS on number processing seem to be inconsistent, likely depending on the polarity of the montage and on the process intended to enhance (e.g., learning vs. automaticity). Concerning polarity, only a bipolar montage with cathodal/anodal tDCS over left/right PPC determined a more consistent improvement in some aspects of number processing compared to the reverse montage (anodal/cathodal over left/right PPC) and the placebo condition ^[19][70]. Concerning the target process, the unsuccessful montage of the aforementioned study (anodal/cathodal over left/right PPC) was found to enhance numerical learning—the acquisition process of numerical information—with a detrimental effect on numerical automaticity performance—the ability to effortlessly process numerical information ^[22][76]. Second, parietal anodal tDCS (regardless of lateralization; right tDCS ^[21][73], right or left tDCS ^[23][74]) and tRNS ^[24][25][77,78] are more likely to obtain improvements in terms of basic numerical processes. When comparing tDCS and tRNS to dlPFC, the application of tES determined positive results in two studies ^[19][26][70,79]; only anodal stimulation over right dlPFC produced a null effect ^[21][73]. Once again, the mixed methodology of the reviewed studies does not facilitate the extraction of the key findings. However, it could be carefully noted that the benefits of prefrontal stimulation on number processing seem to depend on the process intended to enhance. The extracted evidence showed that anodal/cathodal tDCS over left/right dlPFC enhanced numerical automaticity with even a detrimental effect on numerical learning ^[22][76]. Moreover, only sparse evidence of a lateralization-dependent effect was documented with no effect after excitatory stimulation of the dlPFC ^[21][73]. To summarize, both tDCS (regardless of polarity/lateralization) and tRNS (even with only two studies existing) over dlPFC would be advantageous to improve number processing. All but one tRNS study reported positive effects on arithmetic processes (3 out of 4 studies) while tDCS produced 67% of beneficial findings (8 out of 12 studies). In particular, when comparing tDCS and tRNS over parietal regions, the application of tES induced contrasting results in terms of arithmetic process improvement. Specifically, only a bilateral tDCS montage over parietal regions would enhance addition calculation ^[27][28][82,91]. In contrast, the unipolar anodal or cathodal tDCS ^[29][85] and tRNS ^[30][89] did not affect addition performance. Moreover, after applying anodal tDCS over the right hemisphere or anodal/cathodal tDCS over left/right PPC, two studies (respectively, ^[31][32][80,87]) did not find the effects on subtractions and simple multiplication problems. Whereas, after anodal tDCS over left PPC areas, positive effects on mental calculations were obtained (i.e., complex subtraction problems ^[33][93]; double-digit subtraction tasks ^[20][71]; multiplication problems ^[34][81]), especially when the difficulty of the calculation problems increased ^[35][86]. Similarly, the only tRNS study over bilateral PPC ^[36][88] and the one study with a mixed montage (3 days of tRNS over bilateral dlPFC plus 2 days of tRNS over bilateral PPC ^[37][94]) showed positive results on mental calculations regardless of the type (multiplications, additions, and subtractions). The inconsistency of these results could be explained by the high variability of lateralization across individuals during arithmetic tasks. As the study by Kasahara et al. ^[34][81] underlined, the inter-individual variability in functional lateralization across individuals is very high for arithmetic processes, and this variability could contribute to significantly affecting tDCS results. Moreover, another explanation for these mixed results could be the indistinct inclusion of different types of calculations (such as addition, subtraction, and multiplication problems) during stimulations of parietal regions without considering the influence of the tDCS montage polarity. For instance, the study by Hauser et al. ^[32][87] assessed both complex subtractions and simple multiplication problems (i.e., arithmetic facts) as the main numerical cognition outcomes during and after participants receiving anodal/cathodal tDCS over left/right PPC. The authors failed to find some stimulation effects. This null evidence could be explained by some findings showing that, during subtraction and multiplication, left and right parietal regions are differently recruited [6]. Specifically, brain activity seems to be dominant in the bilateral or left hemisphere for subtractions and primarily in the right hemisphere for multiplications [6]. Therefore, when applying tDCS over parietal regions during or after arithmetic tasks, it is important to be particularly cautious to the montage and/or the polarity in light of the lateralization associated with the arithmetic tasks and of the high individual variability. When comparing tDCS and tRNS over dlPFC, studies found that tES significantly enhanced arithmetic processes ^{[28][30][36][38][39]}[83,88,89,91,92] especially when the task was demanding ^[40][84]. Specifically, both bilateral tDCS and tRNS over dlPFC led to consistent improvements ^{[28][36][38][39]}[83,88,91,92]. Similarly, anodal tDCS over left dlPFC was effective in enhancing large subtractions ^[28][91]. The only exception was the null result obtained by Krause et al. ^[41][90], probably because tRNS was proposed to participants who already reached the highest levels of performance (to mathematically highly-proficient, healthy, postgraduate students). Despite methodological heterogeneity across studies, thwe researchers should note that polarity-independent tES, such as tRNS, would more likely result in enhancing certain aspects of arithmetic processes regardless of target brain regions.