历史与综述
The German transcriptions of six letters of Bernhard Riemann preserved in the Smithsonian Libraries (SIL) in Washington DC are given.
Placing regular 4n-sided polygons correctly, equations between sine and sums of sines show up -- exactly these equations are used in B\"urgi's method to approximate sines.
This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference…
We discuss a non-intuitive situation concerning percentages.
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
We survey some major contributions to Riemann's moduli space and Teichm{\"u}ller space. Our report has a historical character, but the stress is on the chain of mathematical ideas. We start with the introduction of Riemann surfaces, and we…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
Based on a previous generalization by the author of Latin squares to Latin boards, this paper generalizes partial Latin squares and related objects like partial Latin squares, completable partial Latin squares and Latin square puzzles. The…
We present some fragments of a teaching experiment realized in a first grade classroom, to sow the seeds for a mathematical definition of rectangles that includes squares. Within the paradigm of semiotic mediation, we studied the emergence…
The aim of this paper is to present a didactical sequence that fosters the development of meanings related to fractions, conceived as numbers that can be placed on the number line. The sequence was carried out in various elementary school…
In this paper we focus on the beginning of publication of the Large Soviet Encyclopedia, launched in 1925. We present the context of this launching and explain why it was tightly connected to the period of the New Economical Policy. In a…
These are reminiscences of I.M.Gelfand's mathematical seminar of 1970s-1980s. The essay will appear in the March 2016 issue of Notices of the AMS.
We study the Neo-Riemannian principle of parsimonious voice-leading using tools and techniques from classical graph theory and the modern field of complex networks. We quantify the relative importance of particular chords within this…
This paper discusses a 100-cell calculation table for addition, C(i,j)=Ai+Bj,(1<=i,j<=10), addressing the special case where the 100 cells C(i,j) comprise continuous numbers 0 through 99. We consider what sequences {Ai,Bj,(1<=i,j<=10)} are…
When compared with pure mathematicians, applied ones have a clear preference for proofs that go beyond a chain of reasonings and do exhibit the fact to be proved. Here we exhibit the bijection between the 60 icosahedron rotations of the…
A simple and popular childhood game, `LOVES' or the `Love Calculator', involves an iterated rule applied to a string of digits and gives rise to surprisingly rich behaviour. Traditionally, players' names are used to set the initial…
We examine Euclid's lemma that if $p$ is a prime number such that $p | ab$, then $p$ divides at least one of $a$ or $b$. Specifically, we consider the common misapplication of this lemma to numbers that are not prime, as is often made by…
These pedagogical lecture notes address to the students in theoretical physics for helping them to understand the mechanisms of the linear operators defined on finite-dimensional vector spaces equipped with definite or indefinite inner…
This is an expository article about the topological theory of digital images, and a gamification of a research project.
To contrast the phenomenon of false positives in the diagnoses of dyscalculia in Italy, among 3rd grade children, a 3-year project (2011-2014), built upon a collaboration between psychologists and mathematics educators, was carried out.…