Related papers: On Arnold's and Pushkin's puzzles

In the following article a Ph.D. student of V.I.~Arnold gives a personal account on his teacher who unexpectedly passed away earlier this year.

In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

In this note I respond to Vilenkin's claim that there must have been a beginning.

Proietti et al. (arXiv:1902.05080) reported on an experiment designed to settle, or at least to throw light upon, the paradox of Wigner's friend. Without questioning the rigor or ingenuity of the experimental protocol, I argue that its…

Written for the book "Mathematicians from Saint Petersburg and their theorems".

Contrary to the opinion of J. Polchinski [Phys.Rev.Lett. {\bf 66}, 397-400 (1991)], the phenomenon of superluminal messages in nonlinear versions of quantum mechanics is not a specific difficulty in a class of theories formulated by S.…

These notes provide an opportunity to discover the beauty of Bourbaki set theory, and I hope that they will facilitate the task to those who find it difficult to read this book, one of the most critical elements of the mathematics of…

In this expository note, we discuss a ``balls-and-urns'' probability puzzle posed by Daniel Litt.

In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the…

Here I give a description of Alexandrov 4-point comparison via quadratic forms and then propose a natural 5-point condition which might have some future. Consider this note as a letter from me --- do not take it seriously.

A short survey about combinatorics on words and algorithmic methods in a ring. Special attention is given to Shirshov's results. Adopted for undegraduate students.

This note is the follow up to a paper by M. Waldschmidt.

In some of his final papers, V.I. Arnold studied pseudorandomness properties of finite deterministic sequences, which he measured in terms of their "stochasticity parameter". In the present paper we illustrate the background in probability…

In this paper we show that a generalized version of the Nikoli puzzle Slant is NP-complete. We also give polynomial time algorithms for versions of the puzzle where some constraints are omitted. These problems correspond to simultaneously…

I gave a geometric proof of Vojta's 1 + epsilon conjecture. Some gaps in the published paper were spotted and kindly pointed out to me by Paul Vojta. These were addressed in "Erratum".

We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

In this note we give the answer to the question posed by V. N. Dubinin concerning covering properties of complex polynomials

Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed.