历史与综述
One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…
This is an English translation of Ludwig Bieberbach's paper ``Remarks on Hilbert's Thirteenth Problem" originally written in German and originally published in Journal f\"ur die Reine und Angewandte Mathematik - 165 (89-92) 1931, along with…
A residue design is an artistic geometric construction in which we have $n$ equally-spaced points on a circle numbered 0 through $n-1$ and we join with a line segment each point $k$ to $ak$ modulo $n$ for some fixed $a\ge 2.$ The envelopes…
This note discusses elliptic functions in Ramanujan's work.
The aim of this paper is i) to argue for the feasibility and fruitfulness of a balance between the phenomenological method seeking intuitive evidence and the axiomatic-deductive method and ii) that there should be a mutual understanding…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
Dessin d'enfants (French for children's drawings) serve as a unique standpoint of studying classical complex analysis under the lens of combinatorial constructs. A thorough development of the background of this theory is developed with an…
Left, Center, Right is a popular dice game. We analyze the game using Markov chain and Monte Carlo methods. We compute the expected game length for two to eight players and determine the probability of winning for each player in the game.…
The purpose of this paper is to present projective geometry in a synthetic, visual and intuitive style through the central notion of harmonicity which leads to harmonic curves. This presentation includes new results, unpublished proofs of…
This paper presents geometric proofs for the irrationality of square roots of select integers, extending classical approaches. Building on known geometric methods for proving the irrationality of sqrt(2), the authors explore whether similar…
We present several ruler and compass practical geometric constructions that can be performed in the lemniscate curve. To be precise, we provide recipes for halving, doubling, adding, subtracting, and transferring lemniscate arcs with ruler…
I prove closed-form identities that I discovered for the first and second derivatives of the $q$-rationals at $q = 1$, in which the $q$-rationals are defined as they are in arXiv:1812.00170.
We survey the combinatorics of the Adinkra, a graphical device for solving differential equations in supersymmetry. These graphs represent an exceptional class of 1-factorizations with further augmentations. As a new feature, we…
In this contribution we revisit a learning laboratory of graph theory, based on the well-known K\"onigsberg's bridges problem due to Euler, already proposed and described in Gaio-Capone-Branchetti (2020): we extend some of its conceptual…
The present document is a mathematical-literary fiction, commemorating the centenary of the death of Anatole France (April 16, 1844 - October 12, 1924) and which, at the same time, pays tribute to Nicolas Bourbaki and his "Godparents".…
Michel Talagrand (Centre National de la Recherche Scientifique, France) has been awarded the prestigious Abel Prize for 2024 for his work in probability theory, functional analysis, and statistical physics. In this note, we introduce the…
Bronze cuboctahedral weights dated to the VIII-X centuries were found in northwest Russia near Ladoga, one of the most important trading centers in Eastern Europe in the VIII-X centuries. The history of the mathematical study of…
This paper is based on the author's talk at the Grothendieck conference at Chapman university on 26-05-2022. It is not a survey of anabelian geometry but rather exposes some of the personal views and experiences of the author with the…
We visualize the identity p(n) = sum s(k) p(n-k)/n for the integer partition function p(n) involving the divisor function s, add comments on the history of visualizations of numbers, illustrate how different mathematical fields play…
This is an English translation of G.N. Chebotarev's paper "On The Klein-Hilbert Resolvent Problem" which was originally written in Russian and published in Izvestiya Kazan. Fiz. Mat. Obshch., 6 (1932-1933), 5-22. In this article, Chebotarev…