It is a fact, that the varying definitions and perspectives on thinking among scientists, emphasizing the influence of theoretical foundations and practical experiences on individual mental processes, would equally highligh the importance of mathematics in developing thinking skills by fostering connections between ideas, organizing information, and encouraging students to record problem-solving strategies. The professional development of mathematics teachers aims to enhance students' thinking abilities by focusing on skills such as problem-solving, abstraction, generalization, and divergent thinking. The use of puzzles and games in education to enhance students' mathematical thinking and problem-solving skills, as a significant indicator on how puzzles and games can engage students in critical thinking, logical reasoning, and creative problem-solving, leading to a deeper understanding of mathematical concepts. By incorporating educational games into teaching, educators can create a fun and interactive learning environment that promotes cognitive, emotional, and psychomotor development in students. On a different note, the potential negative behaviors that can arise from games, such as fraud and deception, when the focus shifts away from educational goals, could be prevented to ensure that games are not solely recreational, do not overly emphasize winning or losing, align with social values, and are understood by students as purposeful educational activities. Additionally, fostering self-efficacy beliefs among students can enhance their persistence and success in achieving goals, as demonstrated in studies using game-based learning environments to improve mathematical skills and motivation. The current exposition showcases the significance of employing puzzles to revolutionize both theory and practice of teaching mathematics. Most potentially, some emerging open problems are provided. The paper ends with some concluding remarks combined with futuristic research pathways.

Artificial Intelligence (AI) has revolutionized the creative process, allowing for novel ways of artistic expression. This paper focuses on the intersection of Abstract Expressionism and AI-generated imagery, exploring how poetic prompts inspire unique visual interpretations. By utilizing Leonardo AI with a medium contrast and leveraging the cinematic kino model/preset, the research demonstrates how simple poetic phrases can yield profound visual artworks. The study evaluates the quality, creativity, and emotional resonance of AI-generated art, offering insights into the synergy between human creativity and machine intelligence within an Abstract Expressionism framework. The Leonardo AI is applied to Ismail A Mageed’s internal monologues in poetic form. The paper ends with some potential open problems and concludes with remarks and future research pathways.

Influential topics in innovative teaching practice of mathematics are covered in this work, namely employing dancing and physical education (PE) as powerful and favourable dynamics to lead innovative mathematics’ teaching. So, by default, the current work briges a unified approach to teach mathemtatics via two interdisciplaries, namely, dancing and physical education. Funadmentally, this paper includes a variety of resources appropriate for scholars, researchers, and students studying mathematics. On another strong note, a plethora of influential open problems are introduced to provide food for thought to the research community to steer ahead a new era of contemporary teaching of mathematics.

As an ultimate generalisation to several kinds of generalised entropy in the literature, a novel entropy measure, namely, Ismail’s entropy, or (IE), is presented. This article spotlights the significance of fractal dimension, through highlighting several possible applications of fractal dimension to structural engineering. In addition to several difficult open problems and the next step of inquiry, the paper ends with some concluding observations.

An exposition is undertaken to analytically validate the credibility of IEF, by investigating the four axioms of consistency on IEF. More fundamentally, IE is by default the ultimate generalization to most entropy measures in the literature. The current paper also provides some applications of Information Theory to 6G Networks. Additionally, the latter review consolidates more foundational motivations and insights into further employment of information-theoretic advancements to 6G networks. Conclusions, open problems, and future directions are given.

Since it is at the centre of important philosophical, physical, and mathematical issues, the notion of infinity has attracted interest and caused controversy for millennia. Focusing on its formal existence in mathematics, its debatable presence in physical reality, and the philosophical debates that these different approaches cause, this paper explores the complicated nature of infinity. Crossing these theoretical barriers enables us to better appreciate how the issue Does infinity exist? does not have a single solution, but rather a range of responses depending on the context of inquiry. Though basic to several fields of abstract thinking and scientific hypothesis, the notion of infinity still presents great and ongoing open questions. Most importantly, This paper presents a brief review of important unsolved issues about infinity appearing in the several but connected fields of mathematics, physics, and philosophy. From the ambiguous nature of the continuum of numbers in mathematics to the contradictions of cosmological models in physics and the ongoing discussion about the reality of actual infinities in philosophy, the infinite keeps pushing the limits of human knowledge and the systems we use to understand the world.