A couple of years ago, a non-mathematician friend of mine who takes an interest in mathematics mainly as puzzles mentioned a problem of Euler.

There remain important questions about how personality shapes risk perceptions, willingness to engage in protective behaviors, and policy preferences during a changing pandemic. Focusing on the Big-5 and COVID-19 attitudes, we find associations between risk perceptions and negative emotionality and agreeableness, as well as between each Big-5 trait and protective behaviors and support for government restrictions. These associations are mostly stable over time, with instability pronounced for lockdown policy support, where agreeableness and conscientiousness diminish in importance as pandemic conditions improve. Negative emotionality, conscientiousness, and agreeableness reduce differences between the political left and right and between those who do and do not trust experts. We highlight the heterogeneous interplay between personality and political ideology to understand pandemic policy support, attitudes, and behaviors.

Computing mathematical expectation for an experiment involving a finite number of numerical outcomes is straightforward. Let X denote the random variable having n possible values x1, x2, x3,…, xn. Letting pk denote the probability of xk, the expected value of X is

$$E\,(X)\, = \,\sum\limits_{k\, = \,1}^n {{x_k}{p_k}} ,$$

which can be interpreted as a weighted average of all xk, where the weight of each outcome is represented by its probability. But caution is required when interpreting the sum if there are infinitely many outcomes and the series fails to converge absolutely.

Large language models based on machine-learning technologies are reshaping linguistic contexts and understandings of language. We explore these reconfigurations by investigating discursive positionings of traditional institutional guardians of power in language in response to these changes. Focusing on the discourse of the Real Academia Española (RAE), we show how RAE’s social functions, ways of asserting authority, and the nature, function, and rightful ownership of RAE’s standard language have been reimagined. Crucially, RAE presents itself as a professional soft power that protects the rights of Spanish speakers. Drawing on tropes of authenticity and endangerment, it conceptualises language generated by machine-learning technologies as inauthentic and as destroying the authentic Spanish of human Spanish speakers. We argue that these discourses are indexical of a power struggle where the role of traditional language norming institutions is reshaped in the face of sociotechnical innovations that are in the hands of global commercial companies. (Standard language, AI technology, language academies, authority in language, big tech, Real Academia Española)*

Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Although for calculations using the number π usually one only needs a few decimal places, mathematicians have devoted much effort to obtain as many decimal places as they have been able to calculate. For a general description of the methods used to approximate the value of π, see e.g. [1, 2].

The literature on cognitive behavioural therapy (CBT) practitioner development suggests that extensive training that monitors adherence and reinforces skilfulness produces increased therapist competence, which is related to better patient outcomes. However, little is still known about how trainees perceive their training and its impact on what they understand to be competent CBT practice. Fifteen trainee and recently qualified CBT practitioners who were taking or had taken a UK BABCP Level 2 CBT training course were recruited and asked to complete a photo elicitation task followed by a semi-structured individual interview. Reflexive thematic analysis resulted in an over-arching theme of training as a personal odyssey, consisting of four main themes: (1) an opportunity to work in a meaningful and interesting profession; (2) a reflective learning process, (3) a well-rounded practitioner, and (4) a worthwhile outcome. The multi-faceted nature of each theme is described and related to existing theory and to author reflexivity. Recommendations are made for ways these findings might be applied to help make CBT training more effective and less demanding, and for future research. Limitations of the study include the preponderance of participants drawn from the NHS Talking Therapies for Anxiety and Depression programme in England and the lack of gender and ethnic diversity.

Key learning aims

1. (1) To understand better the motivation to train, and the experience of training and its outcomes for trainee and recently qualified UK CBT practitioners.

2. (2) To explore what competence in CBT means to participants, and how they evaluate their competence.

3. (3) To describe participants’ perceptions of how training has influenced their own development of competence including the role of the personal and professional selves.

4. (4) To consider practical implications for CBT training.

Taking a feminist critical approach, this paper employs Levinas’s thinking on sensibility and time in Otherwise than being to develop a concept of the body as an original intercorporeality through the fact of having been born which, I argue, provides material depth to his critique of the sovereign subject. Contra Guenther’s (2006) development of a maternal ethics based on Levinas’s assertion that the ethical relation of substitution is “like a maternal body,” I argue that modeling a Levinasian conception of ethics upon the maternal body risks perpetuating normative ideas surrounding motherhood and reproduction. Yet I argue that, apart from a Levinasian conception of ethics, the notion of substitution evokes the situation of pregnancy in which the mother breathes for the fetus. Finally, I conceptualize Levinas’s notion of the oneself as descriptive of all (human) bodies which retain a trace from the body from which they were born. Reading Levinas and Irigaray (2017) together, I argue that the notion of the oneself marks a move from the abstract concept of the subject to the concrete notion of the body as an original intercorporeality whose capacity to breathe autonomously rests upon an immemorial “inspiration” by the body from which it was born.

When first learning about geometric series, students often wonder why these series are termed 'geometric'. The geometry of some geometric series is readily apparent for some common series such as

$$\sum\limits_{n = 1}^\infty{\left( {\frac{1}{2}} \right)}^n = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...{\text{ }}.$$