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The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.
The field of automatic image inpainting has progressed rapidly in recent years, but no one has yet proposed a standard method of evaluating algorithms. This absence is due to the problem's challenging nature: image-inpainting algorithms…
As subjective artistic creations, artistic paintings carry emotion of their creators. Emotions expressed in paintings and emotion aroused in spectators by paintings are two kinds of emotions that scholars have paid attention to. Traditional…
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in…
Our interdisciplinary team Mathematics for Applications in Cultural Heritage (MACH) aims to use mathematical research for the benefit of the arts and humanities. Our ultimate goal is to create user-friendly software toolkits for artists,…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…
The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…
Reviewing Piaget's psychology of reasoning by the mathematical educators of the Federal Republic of Germany late in the 1960th the concept of grouping has been understood similar to a mathematical structure. Possibly to consider empirical…
The interpretation of quantum mechanics known as QBism developed out of efforts to understand the probabilities arising in quantum physics as Bayesian in character. But this development was neither easy nor without casualties. Many ideas…
Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…
Terms such as "affective labor" and "emotional labor" pepper feminist critiques of the workplace. Though there are theoretical nuances between the two phrases, both kinds of labor involve the management of emotions; some acts associated…
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
Mathematics curriculums at most universities tend to perpetuate a belief that higher mathematics is historically and culturally European. First Nations and minority students may not see their identities and cultures reflected in the…
Free translation of the original abstract in Spanish: Some of the most relevant milestones due to, or instigated by, mathematicians concerning the creation, development and advances of Cosmology as a scientific discipline are presented and…
The nineteenth century Russian author Leo Tolstoy based his egalitarian views on sociology and history on mathematical and probabilistic views, and he also proposed a mathematical theory of waging war.
Integrating computation into physics teaching is a curricular move that, at present, has been predominately studied for its cognitive impacts. However, if this modality of instruction shifts how students engage with physics, we argue there…
Infinitesimals have seen ups and downs in their tumultuous history. In the 18th century, d'Alembert set the tone by describing infinitesimals as chimeras. Some adversaries of infinitesimals, including Moigno and Connes, picked up on the…
Graphic statics is undergoing a renaissance, with computerized visual representation becoming both easier and more spectacular as time passes. While methods of the past are revived and tweaked, little emphasis has been placed on studying…