The construct of mathematics anxiety has been an important topic of study at least since the concept of “number anxiety” was introduced by Dreger and Aiken (1957), and has received increasing attention in recent years. This paper focuses on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We discuss what mathematics anxiety is; how distinct it is from other forms of anxiety; and how it relates to attitudes to mathematics. We discuss the relationships between mathematics anxiety and mathematics performance. We describe ways in which mathematics anxiety is measured, both by questionnaires, and by physiological measures. We discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally, we describe some research on treatment. We conclude with a brief discussion of what still needs to be learned.

Psychobiotics were previously defined as live bacteria (probiotics) which, when ingested, confer mental health benefits through interactions with commensal gut bacteria. We expand this definition to encompass prebiotics, which enhance the growth of beneficial gut bacteria. We review probiotic and prebiotic effects on emotional, cognitive, systemic, and neural variables relevant to health and disease. We discuss gut–brain signalling mechanisms enabling psychobiotic effects, such as metabolite production. Overall, knowledge of how the microbiome responds to exogenous influence remains limited. We tabulate several important research questions and issues, exploration of which will generate both mechanistic insights and facilitate future psychobiotic development. We suggest the definition of psychobiotics be expanded beyond probiotics and prebiotics to include other means of influencing the microbiome.

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The surge in noninvasive brain stimulation studies investigating cognitive enhancement has neglected the effect of interindividual differences, such as traits, on stimulation outcomes. Using the case of mathematics anxiety in a sample of healthy human participants in a placebo-controlled, double-blind, crossover experiment, we show that identical transcranial direct current stimulation (tDCS) exerts opposite behavioral and physiological effects depending on individual trait levels. Mathematics anxiety is the negative emotional response elicited by numerical tasks, impairing mathematical achievement. tDCS was applied to the dorsolateral prefrontal cortex, a frequent target for modulating emotional regulation. It improved reaction times on simple arithmetic decisions and decreased cortisol concentrations (a biomarker of stress) in high mathematics anxiety individuals. In contrast, tDCS impaired reaction times for low mathematics anxiety individuals and prevented a decrease in cortisol concentration compared with sham stimulation. Both groups showed a tDCS-induced side effect-impaired executive control in a flanker task-a cognitive function subserved by the stimulated region. These behavioral and physiological double dissociations have implications for brain stimulation research by highlighting the role of individual traits in experimental findings. Brain stimulation clearly does not produce uniform benefits, even applied in the same configuration during the same tasks, but may interact with traits to produce markedly opposed outcomes.

Psychology and microbiology make unlikely friends, but the past decade has witnessed striking bidirectional associations between intrinsic gut microbes and the brain, relationships with largely untested psychological implications. Although microbe-brain relationships are receiving a great deal of attention in biomedicine and neuroscience, psychologists have yet to join this journey. Here, we illustrate microbial associations with emotion, cognition, and social behavior. However, despite considerable enthusiasm and potential, technical and conceptual limitations including low statistical power and lack of mechanistic descriptions prevent a nuanced understanding of microbiome-brain-behavior relationships. Our goal is to describe microbial effects in domains of cognitive significance and the associated challenges to stimulate interdisciplinary research on the contribution of this hidden kingdom to psychological processes.

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Microbes colonise all multicellular life, and the gut microbiome has been shown to influence a range of host physiological and behavioural phenotypes. One of the most intriguing and least understood of these influences lies in the domain of the microbiome's interactions with host social behaviour, with new evidence revealing that the gut microbiome makes important contributions to animal sociality. However, little is known about the biological processes through which the microbiome might influence host social behaviour. Here, we synthesise evidence of the gut microbiome's interactions with various aspects of host sociality, including sociability, social cognition, social stress, and autism. We discuss evidence of microbial associations with the most likely physiological mediators of animal social interaction. These include the structure and function of regions of the ‘social' brain (the amygdala, the prefrontal cortex, and the hippocampus) and the regulation of ‘social’ signalling molecules (glucocorticoids including corticosterone and cortisol, sex hormones including testosterone, oestrogens, and progestogens, neuropeptide hormones such as oxytocin and arginine vasopressin, and monoamine neurotransmitters such as serotonin and dopamine). We also discuss microbiome‐associated host genetic and epigenetic processes relevant to social behaviour. We then review research on microbial interactions with olfaction in insects and mammals, which contribute to social signalling and communication. Following these discussions, we examine evidence of microbial associations with emotion and social behaviour in humans, focussing on psychobiotic studies, microbe–depression correlations, early human development, autism, and issues of statistical power, replication, and causality. We analyse how the putative physiological mediators of the microbiome–sociality connection may be investigated, and discuss issues relating to the interpretation of results. We also suggest that other candidate molecules should be studied, insofar as they exert effects on social behaviour and are known to interact with the microbiome. Finally, we consider different models of the sequence of microbial effects on host physiological development, and how these may contribute to host social behaviour.

The challenge hypothesis makes specific predictions about the association between testosterone and status-seeking behaviors, but the findings linking testosterone to these behaviors are inconsistent. The dual-hormone hypothesis was developed to help explain these inconsistencies. Specifically, according to this hypothesis, testosterone's association with status-seeking behavior depends on levels of cortisol. Here, we (1) describe the dual-hormone hypothesis in relation to the challenge hypothesis; (2) review recent studies that tested the dual-hormone hypothesis as well as meta-scientific evidence of heterogeneous dual-hormone findings across studies; (3) discuss potential explanations for this heterogeneity, including methodological considerations, contextual factors, and individual differences; and (4) provide recommendations for new work aimed at testing and extending the dualhormone hypothesis.