This book is dedicated to the subject “Kolmogorov and Cybernetics”. It can be of interest from various points of view.

First of all, it vividly reflects the personality of Andrey Nikolaevich Kolmogorov, one of the greatest mathematicians of the twenties century, a deep thinker, and an inspired dreamer who tried to anticipate the future of the humankind.

The reader will also be able to sense the romanticism of the early ‘60s when a new generation of Russian scientists first eagerly embraced the ideas of cybernetics. In their youth, just 6 years prior to the famous Kolmogorov’s presentation “Automata and Life” , these scientists could read in the 1954 edition of the Philosophical Dictionary the following definition of cybernetics: “a pseudo-science … directed against the materialist dialectics, contemporary scientific physiology as established by I.P. Pavlov, and marxist , i.e. scientific, understanding of the laws of social life”.

And, finally, the collection as a whole presents a fascinating historical document: many of its materials describe a distinctive period in the development of our country and our science – the time of a sudden turn in the historical fortune of a whole nation, the time that brought new hopes and a change of generations in mathematics.

All the above becomes especially important during this first year of the century, indeed of new millenium: the time to sum up the past, the time to think of the future.

The title of this collection coincides with the title of a paper included in it and written by Ya.M. Barzdin and R.V. Freiwald as a result of the 6th All-Union Conference on Theoretical Cybernetics held in Gorky (now Nizhni Novgorod) in 1988. This paper is published for the first time and is somewhat abridged by agreement with the authors. We will let the reader decide whether the issues raised in it are still relevant more than a decade later.

The central position in this book is occupied by materials related to A.N. Kolmogorov’s presentation “Automata and Life” which was delivered on April 6, 1961 at Moscow State University as well as by some publications that followed this event. N.G. Khimchenko (Rychkova), the author of an abridged version of the report published in the “Tekhnika – Molodezhy” magazine, put in a lot of effort in order to clear the text of simplifications made by the editorial staff. This well known and repeatedly published report is now appearing precisely as in was first submitted to the magazine with Kolmogorov’s “blessing”. Thoroughly verified were also the “Theses” that Andrey Nikolaevich personally wrote for the presentation. The details of this work are discussed by N.G. Khimchenko in her note “The way it was…“.

Quite surprisingly, when this collection was already put, two almost incredible events happened. First, Ya.I. Fet discovered in A.A. Lyapunov’s archives a letter sent by A.N. Kolmogorov to A.A. Lyapunov which enclosed, as a topic to be discussed, Kolmogorov’s letter to A.I. Berg who at the time was the Chairmen of the Council on Cybernetics. The letters discuss publications closely relater to the report “Automata and Life”. The second discovery was made by A.N. Shiryaev who found in Kolmogorov’s home archives a yellowed folder designated, in Andrey Nikolaevich’s hand, «My presentation “Automata and Life”». The folder contained, besides the “Theses”, 24 notes sent by the audience during the presentation itself. Needless to say that the editors included all these materials in their collection.

The collection begins with another exiting project, a preliminary version of an A.N. Kolmogorov’s Web page. At present, the students of Andrey Nikolaevich are reviewing the page and providing their inputs. After this work is completed, the page can be found in the Internet. We will appreciate any comments from the readers concerning these materials.

Finally, the editors have included a few words of my own on the subject “Kolmogorov and Cybernetics” written especially for this publication.

Concluding this brief introduction, I would like to express my hope that the reader will be impressed by the materials of this collection . Let me also wish the creators of this Series a lot of success in their noble efforts.

V. Tikhomirov