历史与综述
Annotated parallel text in Latin and English of the paper of Adam Adamandy Kocha\'nski "Solutio Theorematum Ab illustri Viro in Actis hujus Anni Mense Januario, pag. 28. propositorum", Acta Eruditorum, Lipsiae 1682, pp. 230-236, in which he…
Annotated parallel text in Latin and English of the classic paper of Adam Adamandy Kocha\'nski "Observationes Cyclometricae", published in Acta Eruditorum 4:394--398 (1685), in which he presented approximate geometric method of…
This is an English translation of Anders Wiman's classical paper "\"{U}ber die Anwendung der Tschirnhausen Transformation auf die Reduktion algebraischer Gleichungen" from 1927. The original work first appeared in the 1927 extraordinary…
We present here a simple mathematical model that provides a successful strategy, quantitatively, to ending the continued championship futility experienced by Canadian Hockey Teams. Competitive Intransitivity is used here as a simple…
In 1888, Heinrich Schroeter provided a ruler construction for points on cubic curves based on line involutions. Using Chasles' Theorem and the terminology of elliptic curves, we give a simple proof of Schroeter's construction. In addition,…
The shortest known proof of the law of quadratic reciprocity (without supplements) is presented.
A discussion about conditions on the profiles of voters in order to avoid contradictory decisions that have been designed by Sen and others.
After a quick exposition of Mazzola's quantum modulation model for the so-called triadic interpretation of the major scale within the equal temperament, we study the model for the tetradic interpretation of the same scale. It is known that…
Herman Melville's novel Moby-Dick contains a surprising number of mathematical allusions. In this article we explore some of these, as well as discussing the questions that naturally follow: why did Melville choose to use so much…
It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the…
Theory Building has been largely ignored in Mathematics Education, especially at the Middle and High School Levels. This thesis focuses on Assumption Digging, a type of Theory Building similar to what Hilbert undertook in his Grundlagen…
These notes stem from lectures given by the first author (JM) at the 2008 "Moonshine Conference in Kashiwa" and contain a number of new perspectives and observations on Monstrous Moonshine. Because many new points have not appeared anywhere…
Notice that the square of $9376$ is $87909376$ which has as its rightmost four digits $9376$. To generalize this remarkable fact, we show that, for each integer $n\ge 2$, there exists at least one and at most two positive integers $x$ with…
In his Untersuchungen zur allgemeinen Axiomatik (1928) and Abriss der Logistik (1929), Rudolf Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate…
How can we convince students, who have mainly learned to follow given mathematical rules, that mathematics can also be fascinating, creative, and beautiful? In this paper I discuss different ways of introducing non-Euclidean geometry to…
In this paper, dedicated to the memory of Kirill Mackenzie, I relate the origins and early development of the theory of graded Lie brackets, first in the publications on differential geometry of Schouten, Nijenhuis, and…
The theme of the influence of Bourbaki's ideas and methodologies on disciplines that transcend the mathematical field has been frequently addressed and, in particular, the reflection on the relationship between Bourbaki and Oulipo has…
In this article, I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us (the…
The article is dedicated to recalling the life and mathematics of Louis Nirenberg, a distinguished Canadian mathematician who recently died in New York, where he lived. An emblematic figure of Analysis and Partial Differential Equations in…
This paper is an introduction to our ongoing more comprehensive work on a critically important period in the history of Russian mathematics education; it provides a glimpse into the socio-political environment in which the famous Soviet…