Related papers: Shall We (Math and) Dance?
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
Category Theory provides us with a clear notion of what is an internal structure. This will allow us to focus our attention on a certain type of relationship between context and structure.
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
"Is math useful?" might sound as a trick question. And it is. Of course math is useful, we live in a data-filled world and every aspect of life is totally entwined with math applications, both trivial and subtle applications, of both basic…
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…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
Choreographer Reggie Wilson and mathematician Jesse Wolfson describe interactions of math and dance emerging from their 12+ year engagement with Black movement and music traditions as part of Wilson's…
After presenting the general framework of 'mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's hexachordal theorem. We briefly…
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to…
Category theory has become central to certain aspects of theoretical physics. Bain [Synthese, 190:1621--1635 (2013)] has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Category theory provides a collective description of many arrangements in mathematics, such as topological spaces, Banach spaces and game theory. Within this collective description, the perspective from any individual member of the…
The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…