Related papers: On Arnold's and Pushkin's puzzles
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
This is an English translation of the paper in which N. I. Akhiezer discovered his famous orthogonal polynomials on two intervals in a connection with a generalization of the Korkin-Zolotarev (Korkine-Zolotaref) problem (see the small…
This paper presents correspondence between Albert Einstein and the mathematical analyst J. L. B. Cooper on the Einstein-Podolsky-Rosen (EPR) paradox of quantum theory published in 1935. Two letters written by Cooper, and the replies from…
Remarks on the life and work of Paul Erdos.
These are the notes (in French) for a Bourbaki talk on the twisted Lang-Weil estimates of Hrushovski, following a recent proof of Shuddhodan and Varshavsky.
The comments relate to the often overlooked, if not in fact intentionally disregarded depths of what the so called internal aspects of mathematical knowledge may involve, depths concerning among others issues such as its unreasonable…
This paper puts forward an ontology that is indebted to QBism, Kant, Bohr, Schr\"odinger, the philosophy of the Upanishads, and the evolutionary philosophy of Sri Aurobindo. Central to it is that reality is relative to consciousness or…
We compare the results of our earlier paper on the floating in neutral equilibrium at arbitrary orientation in the sense of Finn-Young with the literature on its counterpart in the sense of Archimedes. We add a few remarks of personal and…
This is a short apology of the style of the Elements by Euclid and Bourbaki.
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
We investigate a coin-weighing puzzle that appeared in the Moscow Math Olympiad in 1991. We generalize the puzzle by varying the number of participating coins, and deduce an upper bound on the number of weighings needed to solve the puzzle…
It is remarked that Dave Robbins's Expression for the integral of an alternant over the unit simplex (math.CO/9805108) follows immediately from an excercise in Polya-Szego.
We give a new construction of the one-variable Alexander polynomial of an oriented knot or link, and show that it generalizes to a vector valued invariant of oriented tangles.
The aim of these notes is to explain main ideas of the theory of complements. Basically we will follow Shokurov's work alg-geom/9711024.
Two theorems and one conjecture about nodal sets of eigenfunctions arising in various spectral problems for the Laplacian are reviewed. It occurred that all these assertions are incorrect or only partly correct, but their analysis has…
Generalizing work of Marin [12], we construct in a unified way all the "braids and ties'' algebras available in literature and new ones.
In the context of partially ordered vector spaces one encounters different sorts of order convergence and order topologies. This article will investigate these notions and their relations. In particular we study and relate the order…
Do bilingual Russian-French authors of the end of the twentieth century such as Andre\"i Makine, Val\'ery Afanassiev, Vladimir F\'edorovski, Iegor Gran, Luba Jurgenson have common stylistic traits in the novels they wrote in French? Can we…
We settled a conjecture of Feigin, Wang and Yoshinaga, appeared in the preprint "Integral expressions for derivations of multiarrangements" (arXiv: 2309.01287v2).
We give a survey of geometric methods used in papers and books by V.I.Arnold and by V.V.Kozlov. They are methods of different normal forms, of different polyhedra, of small denominators and of asymptotic expansions.