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The purpose of this paper is to establish necessary and sufficient optimality conditions and some duality results for weakly efficient solutions of a constrained bilevel multiobjective fractional programming problem (P) with an extremal-value function. Using parametric approach, the problem (P) is first equivalently transformed into a parametric problem (P µ) with µ ∈ Rp, for which we construct then a dual problem. This is achieved in terms of conjugate duality theory. Under appropriate assumptions, the weak and strong duality results for (Pµ) are presented. These results permit us to give dual characterizations for the weakly efficient solutions of the problem (P).

Physical activity provides numerous benefits to physical and mental health, even affecting learning. Despite this, one of the main modern problems is represented by sedentariness. Children and adolescents spend most of their time at school. Therefore, a valid teaching methodology to benefit from the positive effects of physical activity and reduce sedentary moments could be interdisciplinary learning, which integrates physical education into various curricular subjects. Specifically, this paper proposes a systematic literature review of some protocols (n = 11) to investigate whether an elementary school’s integrated physical education and mathematics curriculum can improve learning in the logic-cognitive domain. From all the studies reviewed, the strong importance of interdisciplinary teaching, linking mathematics to physical education, was confirmed to reduce sedentary moments and enable a better attitude toward this discipline, breaking down the many stereotypes that often paint it as a complex and abstract subject.

The paper proposes a reflection on mathematical beauty, considering the possibility of aesthetic qualities for formal language. Through a concise overview of the way this question is understood by some famous scientists and mathematicians, we turn our attention to Gian-Carlo Rota’s theoretical proposal: his reflections as a mathematician and philosopher offer a perspective, of phenomenological matrix, fruitful for looking at the question. Rota’s contribution allows us to focus on the role of competence, acquired through effort, sedimentation and habit of repetition, in cultivating the potential to recognise the aesthetic quality of formal language. Finally, we draw on some contributions from Gestalt theory, closely connected to twentieth-century phenomenology for chronological and conceptual reasons, applying the idea of gestalt wholeness to the mathematical product and proposing some reflections that may help to clarify some of the dynamics underlying the attribution of qualities of beauty to formulas or the detection of its lack.