Related papers: In praise (and search) of J. V. Uspensky

This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…

This paper is a top down historical perspective on the several phases in the development of probability from its prehistoric origins to its modern day evolution, as one of the key methodologies in artificial intelligence, data science, and…

We explore an (unpublished) approach to the famous Jacobian Conjecture by means of identities of algebras, discovered by the brilliant deceased mathematician, Alexander Vladimirovich Yagzhev (1951{2001). This approach also indicates some…

An informal and elementary introduction to probability scoring and forecast verification and improvement, slightly extended from Significance 22:3(2025)16, which might be useful for less mathematical readers as a prologue to the classic…

In celebration of Professor Ron Doney's 80th birthday, we provide a summary of his academic career and contributions to probability theory, as one of the UK's leading probabilists for over 50 years. A version of this note also serves as an…

Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its…

This book contains a large number of exercises related to different stochastic disciplines. Difficulty of the problems varies from the basic level in the first chapter up to the analysis of articles in Probability, Statistics and Computer…

This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…

This issue contains, in addition to the usual contents, a special festive announcement: A book. This book by Banakh and Zdomsky seems to be the first in a planned series by these authors. We believe that the book will become a cornerstone…

With the approaching TOPOSYM'16 (http://www.toposym.cz/programme.php), it is a pleasure to see selection principles gain increasing attention and becoming a standard part of topology and set theory. At least eight of the 28 speakers, and a…

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

A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…

This is a historical introduction to the theory of Stirling numbers of the second kind S(n,k) from the point of view of analysis. We tell the story of their birth in the book of James Stirling (1730) and show how they mature in the works of…

Recent developments of affine algebraic geometry, especially the theory of open algebraic surfaces, provide means to systematically explore geometric and topological properties of polynomials in two variables. Nevertheless, there is one…

This paper is an introduction to our ongoing more comprehensive work on a critically important period in the history of Russian mathematics education; it provides a glimpse into the socio-political environment in which the famous Soviet…

We survey emigration of mathematicians from Europe, before and during WWII, to Russia.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

The first half of the 20th century in the history of Russian mathematics is striking with a combination of dramaticism, sometimes a tragedy, and outstanding achievements. The paper is devoted to St. Petersburg-Leningrad Mathematical School.…

As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…