Related papers: Mathematics, Love, and Tattoos
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
In three articles published in CNJ in 2012 and 2016 , we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation of this cycle. It tells the story of selected important developments…
Mathematics has become inescapable in modern, digitized societies: there is hardly any area of life left that isn't affected by it, and we as mathematicians play a central role in this. Our actions affect what others, in particular our…
Rotated reference frames offer fast algorithms for the radiative transport equation (RTE). We review the singular-eigenfunction approach and related numerical methods for the multi-dimensional RTE with rotated reference frames.
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
K. Kato has recently defined and studied heights of mixed motives and proposed some interesting questions. In this paper, we relate the study of heights to the study of Tamagawa numbers of motives. We also partially answer one of Kato's…
We survey certain accessible aspects of Grothendieck's theory of motives in arithmetic algebraic geometry for mathematical physicists, focussing on areas that have recently found applications in quantum field theory. An appendix (by Matilde…
Mathematical aspects of contemporary classical and quantum gauge theory are sketched.
Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and…
Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…
The concept of number and its generalization has played a central role in the development of mathematics over many centuries and many civilizations. Noteworthy milestones in this long and arduous process were the developments of the real…
The paper discusses relationships between aesthetics theory and mathematical models of mind. Mathematical theory describes abilities for concepts, emotions, instincts, imagination, adaptation, learning, cognition, language, approximate…
This is a former PhD student's take on his teacher's scientific philosophy. I describe a set of 'principles' that I believe are conducive to good applied mathematics, and that I have learnt myself from observing Hans van Duijn in action.
We report on the numerical implementation of thin film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus…
This is an expository article about the topological theory of digital images, and a gamification of a research project.
In his scientific treatise entitled De Lineis, Angulis et Figuris, seu Fractionibus et Reflexionibus Radiorum, Robert Grosseteste is discussing some qualitative geometric rules about reflection and refraction. However, he is also discussing…
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational mathematics suggested by an analytical (not compositional)…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
The Riemann-Roch formula is a cornerstone in the classical theory of algebraic curves. Here we present a novel approach to its proof, by answering a question posed in 2007 by Matthew Baker and Serguei Norine.