历史与综述

Kaleidoscope-roulettes, a proper class of perception games, is described. Kaleidoscope-roulette is defined as a perception and, hence, verbalizable interactive game, whose hidden dialogue consists of quasirandom sequences of ``words''. The…

The interactive game theoretical approach to the description of perception processes is proposed. The subject is treated formally in terms of a new class of the verbalizable interactive games which are called the perception games. An…

A problem from Democritus is used to illustrate the building, and use, of infinitesimal covectors from its regularized, finite, counterpart.

The note is devoted to an interactive game theoretic formalization of dialogues as psycholinguistic phenomena and the unraveling of a hidden dialogue structure of 2-person differential interactive games. In the field-theoretic description…

Procedures of the short-term predictions for processes in general 2-person differential interactive games are proposed. Their effectiveness is discussed.

An important class of differential interactive games, namely, one of the laced interactive games is considered. A posteriori analysis of such games (including the virtual a posteriori decomposition of a collective control) is discussed.…

The title says it all

Many important journal functions would be lost if the mathematical community replaced all paper journals with electronic media. Electronic media are useful for some purposes, but they will not be the basis for a publishing revolution in the…

I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.

Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer\'edi's theorem is presented.

This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…

In this paper we give an additive representation of the factorial, which can be proven by a simple quick analytical argument. We also present some generalizations, which are linked, on the one hand to an arithmetical theorem proven by Euler…

Conventional wisdom in baseball circles holds that a seven-game playoff series is fairer than a five-game series. In an earlier paper, E. Lee May, Jr. showed that, treating each game as an independent event, a seven-game series is not…

Given a right triangle and two inscribed squares, we show that the reciprocals of the hypotenuse and the sides of the squares satisfy an interesting Pythagorean equality. This gives new ways to obtain rational(integer)right triangles from a…

Presents a history of the evolution of the author's ideas on program-size complexity and its applications to metamathematics over the course of more than four decades. Includes suggestions for further work.

We rewrite Riemann Zeta function as a sum over the primes. Each term of the sum is a product that depends only on the summation index (a prime) and the primes following it.

A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by…

This is a brief overview of some turning points in the history of infinitesimals.

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…