历史与综述
We address certain structural innovations in the music of Claudio Monteverdi, which defined the pivotal transition from the Renaissance prima pratica to the Baroque seconda pratica. To formalize this analysis, we employ Mazzola's…
This is a review (in Italian) on aperiodic tilings of the plane intended for a general audience. First, we recall some basic results about lattices and periodic tilings. Then, we move on to one-dimensional (domino) tilings and Wang tilings.…
Here, we give a self-contained and elementary proof of a minimax theorem due to Fan in a simplified setting that can be taught in an advanced undergraduate course. Our proof follows Nikaido's argument with some simplifications.
We discuss the significance of some interesting results by Barbara Rokowska about combinatorial constructions. Her interest in finite mathematics and number theory began with an embellishment and detailing of some work by Erdos. Rokowska…
A class of numerical quadrature rules is derived, with equally-spaced nodes, and unit weights except at a few points at each end of the series, for which "corrections" (not using any further information about the integrand) are added to the…
Despite of the fact that the Damped Wave and the Heat equations describe phenomena of distinct nature, it is amazing that their solutions are related in the limit as $t \to \infty$. The aim of this note is to explain to undergraduate…
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics…
I argue against the predominant view of Weyl's interpretation of the logical signs. Drawing on his correctness-first account of mathematical knowledge, I point out that, according to him, quantified statements generate conditional…
Written for the book "Mathematicians from Saint Petersburg and their theorems".
We review Mabry's, Edgar's, and the Viewpoints 2000 Group's proofs without words for the geometric series formula. Mabry and Edgar proved without words that $$\frac{1}{4} + \left(\frac{1}{4}\right)^2 + \left(\frac{1}{4}\right)^3 + \cdots\…
This reform was a part of a transnational movement as 'the New Math' in the United States or the activity of the Lichnerowicz commission in France. The Russian version of these events involved the whole secondary and high school (4-10…
It has often been said, correctly, that a monkey forever randomly typing on a keyboard would eventually produce the complete works of William Shakespeare. Almost just as often it has been pointed out that this "eventually" is well beyond…
This text is written in remembrance of Vladimir (Volodia) Sidorenko, honoring his scientific work, his kindness, and the warm and humorous spirit he brought into the community.
This dissertation studies the Fourier restriction, which is to find the range of the constants p, q such that the L^q norm on a chosen subset of the Fourier domain is bounded above by the L^p norm in a spacial domain, up to some constant…
This is a critical response to some arguments and general recommendations presented in a discussion paper Four Levels of Ethical Engagement [EiM Discussion Paper 1/2018 University of Cambridge Ethics in Mathematics Project,…
The goal of this book is to provide an introduction to the mathematical theory of Kinetically constrained models developed in the last twenty years, intended for both mathematicians and physicists.
The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.
This paper shares a classroom story from Fall 2022 to Spring 2025 about a learner centered routine in undergraduate mathematics. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a…
An infinite continued composition is an expression of the form \begin{equation*} \lim_{n\to\infty}t_0\circ t_1 \circ t_2 \circ \cdots \circ t_n(c)\;, \end{equation*} where the $t_i$ are maps from a set $D$ to itself, the initial value $c$…
We observe that the computation $5^2 = 25$ has the digital property of the result being equal to the exponent concatenated directly to the left of the base. The generalization to a Diophantine equation and inequality in number bases has…