历史与综述
Our question is ``What is the probability that at least three members of the senate share the same birthday?'' Before the pandemic, I asked this question in several popular math talks I gave at universities across the country. Inspired by…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
These are the second 50 issues of This Week's Finds of Mathematical Physics, from April 23, 1995 to March 23, 1997. These issues discuss quantum gravity, topological quantum field theory and other topics in mathematics and physics. They…
It has been known for more than 300 years that the shape of an inelastic hanging cable, chain, or rope of uniform linear mass density is the graph of the hyperbolic cosine, up to scaling and shifting coordinates. But given two points at…
We re-create the essential results of a 1989 unpublished article by Mazzola and Muzzulini that contains musicological aspects of a first-species counterpoint model. We include a summary of the mathematical counterpoint theory and several…
Ellipses, parabolas and hyperbolas all have beautiful reflective properties. However, an intuitive explanation for why they have those properties has been lacking. There exist many mathematical proofs, but they tend to involve several…
These are the first 50 issues of This Week's Finds of Mathematical Physics, from January 19, 1993 to March 12, 1995. These issues focus on quantum gravity, topological quantum field theory, knot theory, and applications of $n$-categories to…
We build solutions in $\mathbb{Z}[i]$ of $A^{5}+B^{5}=C^{5}\pm 1$ based on a method developed by Michael D. Hirschhorn in his article "An Amazing Identity of Ramanujan", from Mathematics Magazine, Vol. 68, No3 (June 1995).
The definition of who is or what makes a ``mathematician" is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered…
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
Disagreements that resist rational resolution, often termed ``deep disagreements'', have been the focus of much work in epistemology and informal logic. In this paper, I argue that they also deserve the attention of philosophers of…
This is an English translation of six articles, originally written in Ukrainian, by the semigroup theorist Anton Kazimirovich Sushkevich (1889-1961). The articles date between 1935 and 1939, and were all written in Kharkiv. A preface is…
This text is based on my talk at the popular science conference ``Dark geometry fest'' which was related to geometric methods and their applications, July 17, 2022. We will move towards the Smale-Hirsch theorem. To this end we will deal…
Math anxiety negatively relates to math performance. This negative relationship may be exacerbated in low-progress math learners. However, there are limited studies on math anxiety among low progress learners in a paradoxically high…
This paper provides an overview of the Pythagorean centrality measures, which are the arithmetic, geometric, and harmonic means. Both the evolution of their meaning through history and their geometrical interpretation are outlined. Relevant…
Math anxiety is a highly prevalent problem in education that has consistently shown to lead to poor math performance. This study sought to investigate whether certain behaviours are predictive of math anxiety among students. This study…
This study concerns the use of e-learning in the mathematics education system, shedding the light on its advantages and disadvantages, analyzing its applicability either partially or totally, and discussing the ways of improvement. From…
The received Hilbert-style axiomatic foundations of mathematics has been designed by Hilbert and his followers as a tool for meta-theoretical research. Foundations of mathematics of this type fail to satisfactory perform more basic and more…
Mark Kac asked a famous question in 1966 entitled Can one hear the shape of a drum?, a spectral geometry problem that has intrigued mathematicians for the last six decades and is important to many other fields, such as architectural…