历史与综述
I provide for the first time in English a line-by-line translation of the entire text of the monumental 1840 memoir of Olinde Rodrigues, "On the geometrical laws governing the motions of a solid system..." published in French in the Journal…
The year 1954 marks the beginning of a tradition of workshops at the MFO in the area of finite group theory. This is highlighted and put into context in this article (contribution to a book).
Inspired by a didactic experience in an academic environment, and following the idea given by M. Villa in \cite{Villa}, we illustrate two different proofs of an important result in Euclidean geometry studied in the first two years of…
This text offers a personal account of the scientific legacy of two giants of mathematical physics at the turn of the Millenium and their heritage in Canada, their land of adoption.
In this paper we discuss, from a historical and philosophical point of view, a variation of the meaning of the five postulates in Euclidean Geometry and we make a short reference to D. Hilberts formalism. We examine, throughout the ages,…
We give a few examples of Chebyshev polynomials that appeared in mathematical problems from the 16th and 17th century. The main example is the famous equation of Adrianus Romanus (Adriaan van Roomen) containing a polynomial of degree $45$.
The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. In this paper, we offer a descriptive theory of…
Recent years have seen spectacular progress in the mathematical study of hydrodynamic equations. Novel tools from convex integration in particular prove extremely versatile in establishing non-uniqueness results. Motivated by this…
This is an English translation of Ostrowski's article "\"Uber Dirichletsche Reihen und algebraische Differentialgleichungen" published German in Math. Zeit. vol. 8, 1920, pp. 241-298. In this article, Ostrowski proves a conjecture of…
Joseph-Nicolas Delisle was one of the most important scientists at the Saint Petersburg Academy of Sciences during the first period when Euler was working there. Euler was helping him in his work on astronomy and in geography. In this…
Paul Lorenzen, mathematician and philosopher of the 20th century, mentions October 1947 as the date of a crisis in his mathematical and philosophical investigations. An autograph dated 15 October 1947 documents this crisis. This article…
The Fibonacci numbers are familiar to all of us. They appear unexpectedly often in mathematics, so much there is an entire journal and a sequence of conferences dedicated to their study. However, there is also another sequence of numbers…
This proof without words demonstrates that there are $\binom{n+2}{4}$ equilateral triangles in the regular $n$-vertices-per-side triangular grid by describing a map from four-element subsets of $\{1,2, \dots, n+2\}$ into the set of…
This paper presents the construction and some properties of the Kochawave curve, a simple and asymmetrical variant of the Koch curve.
In his first mathematical paper, published in 1895 when he was 18, Edmund Landau suggested a new way to determine the winner of a chess tournament by not simply adding for each player the fixed number of points they would get for each win…
By introducing various actions involving color to geometrical objects, we represent a cube and simplex in four or fewer dimensions, the geometrical net of a cube and simplex in five or fewer dimensions, hyperprisms, truncated polytopes,…
We study the twisting fault emerging in circular knitting and its relation to the mathematical concepts of framing curves and the Gauss linking integral. We create three knitted bands with framing zero, one, and negative two, and use three…
The objective of this article is to investigate the effect of active-learning pedagogy on learners' academic achievement and their attitude toward mathematics using both quantitative and qualitative methods. We cultivated sustainable…
In this volume, we encouraged a broad array of submissions that highlight issues of Diversity, Equity, and Inclusion (DEI) in introductory mathematics programs with special attention to precalculus, differential calculus, and integral…
Let $p$ be a prime number. As a standard application of the irreducibility criterion of Eisenstein, it is well known that the $p$-th cyclotomic polynomial $\Phi_p(t)=1+t+\dots+t^{p-1}$ is the minimal polynomial of $e^{2\pi i/p}$ over…