We are all familiar with the formulae for finding the sums of the powers of the first n natural numbers. For example,

In contrast to Western platforms, which are dominated by crowdsourced labour, China's food-delivery platforms rely heavily on outsourced couriers to provide high-quality services. The conflicts emerging from outsourced labour relations have been inadequately examined. Based on extensive fieldwork in south China, this study reveals an intriguing fact: the outsourcing model frequently triggers yet largely conceals couriers’ strikes. This study uses the work regime approach and labour bargaining power theory to analyse the complex dynamics created by the platforms. By scrutinizing state institutions, relationships among various organizations and workplace interactions, this study finds that the platform firms have dominant power but that inherent tensions exist between outsourcing platform firms, outsourced agencies, human supervisors and workers, forming a regime that this study calls “contentious despotism.” Importantly, labour conflict is alive and potentially enduring in China's gigantic platform economy.

For every $r\in \mathbb {N}_{\geq 2}\cup \{\infty \}$, we prove a $C^r$-orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with one-dimensional orientation preserving center bundle. To be precise, for such a diffeomorphism f, if a point y is chain attainable from x through pseudo-orbits, then for any neighborhood U of x and any neighborhood V of y, there exist true orbits from U to V by arbitrarily $C^r$-small perturbations. As a consequence, we prove that for $C^r$-generic diffeomorphisms in this class, periodic points are dense in the chain recurrent set, and chain transitivity implies transitivity.

The pressures currently on teachers of mathematics at every level seem greater than ever, whether that is university mathematics lecturers, school teachers or those who work with very young learners. So, I began my Presidential Address with the hope that no one would leave the Joint Conference of Mathematics Subject Associations 2023 feeling as though they were not good enough and must do more. I did not want anyone to go home with a lengthy to-do guilt list of additional things they must try to incorporate into their practice. Instead, I advocated giving attention to the ancient proverb “less is more”, versions of which are found within many cultures; e.g., “brevity is the soul of wit” (Hamlet), “Sometimes diminishing a thing adds to it; Sometimes adding to a thing diminishes it” (Tao Te Ching). I offered five aspects of mathematics teaching and learning that might benefit from ‘less of’ something, in each case trying to see how this might create space for more of something else. In this article, I present these five suggestions for improving by removing.