历史与综述
A probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon…
In 1512, on December 30, the first edition of Fray Juan de Ortega's Arithmetic was published in Lyon. The last chapter, titled "Rules of Geometry", deals with lower approximations of 14 square roots. In later editions of the Arithmetic on…
In this article, we present a short, non-exhaustive study of an important and well-known property of combinatorial sequences - unimodality. We shall have a look at a sample of classical results on unimodality and related properties, and…
This is an English translation of "The Resolvent Problem" by Tschebotarow/Chebotarev. In this article, Chebotarev summarizes the history of the resolvent problem from compass and ruler constructions to Klein and Hilbert' formlutions of the…
We describe the Fundamental Theorem on Symmetric Polynomials (FTSP), exposit a classical proof, and offer a novel proof that arose out of an informal course on group theory. The paper develops this proof in tandem with the pedagogical…
The ruler function or the Gros sequence is a classical infinite integer sequence that is underlying some interesting mathematical problems. In this paper, we provide four new problems containing this type of sequence: (i) a demographic…
In this manuscript a joint project between young researchers from all around the world, the Intercultural Science-Art Project, is presented, in which all participants interpreted their own research with art. Art is meant in the most…
In ancient times, China made great contributions to world civilization and in particular to mathematics. However, modern sciences including mathematics came to China rather too late. The first Chinese university was founded in 1895. The…
Suppose that you're going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer - possibly much longer - than what the bus schedule suggests intuitively. This phenomenon,…
There is a relationship between the Borromean rings, the icosahedron and something called the Poincar\'e homology sphere. This relationship is explored in a wandering path that introduces fundamental ideas from topology and a geometric…
Sumterms are introduced as syntactic entities, and sumtuples are introduced as semantic entities. Equipped with these concepts a new description is obtained of the notion of a sum as (the name for) a role which can be played by a number.…
Frierson used a powerful parameterization of the pattern of the order 3 associative magic square to construct a family of six related order 9 compound (or composite) magic squares, several of them ancient. Stimulated by Bellew's 1997…
In his famous work, "Measurement of a Circle," Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern…
This evocative essay focuses on some landmarks that led the author to the study of principal curvature configurations on surfaces in $\mathbb R^3$, their structural stability and generic properties. The starting point was an encounter with…
This paper, originally written in Hungarian by D\'{e}nes K\H{o}nig in 1931, proves that in a bipartite graph, the minimum vertex cover and the maximum matching have the same size. This statement is now known as K\H{o}nig's theorem. The…
Barry Mazur published an article some year ago, where he showed, among other things, that the result in the so-called mathematical passage of Plato s Theatetus and Euclid s proposition X.9 in the Elements are very different, while almost…
Using the definition of quasiperiodic function as a motivation, we introduce the idea of quasiperiodic music and detail the composition process of a quasiperiodic music piece, Raindrops in A minor. We also discuss connections between…
Scientists use a mathematical subject called 'topology' to study the shapes of objects. An important part of topology is counting the numbers of pieces and holes in objects, and people use this information to group objects into different…
I will consider some questions related to Euler's work on cartography and its consequences, in which the foliations of the sphere by meridians and parallels play important roles.
Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information…