The year of 1957 will remain in the memory of mankind as the date of the first artificial satellite launched to orbit the Earth. It is the same year that the Siberian Division of the Academy of Sciences sprang into being in Russia. These outstanding instances of the successful implementation of large-scale projects are listed in the treasure trove of the Russian culture. The recent state decision of founding a technopark in Akademgorodok near Novosibirsk has become a new impetus for the Siberian Division of the Russian Academy of Sciences. We are at the threshold of the drastic changes in the life of the Siberian Division as well as the whole of the Russian Academy of Sciences. The main challenges of the scientists of the present days stem from the deep national crisis and decay that require the safeguarding and preserving of science and education in this country. The history of foundation and development of the Siberian Division brings about the great stock of scientific, managemental, and moral experience so necessary in the hard times of choosing new ways and decisions.
The basic principles of the founders of the Siberian Division were the prevalence of the fundamental science and the understanding of the specific role of all branches of exact knowledge, primarily of mathematics.
Mathematics is the most ancient of sciences. However, in the beginning was the word. We must remember that the olden “logos” resides beyond grammar. Today’s mathematics became the bastion of logic, the savior of the order of mind and the objectivity of reasoning.
The intellectual field resides beyond the grips of the law of diminishing returns. The more we know, the huger become the frontiers with the unbeknown, the oftener we meet the mysterious. The twentieth century enriched our geometrical views with the concepts of space-time and fractality. Each instance of knowledge is an event, a point in the Minkowski 4-space. The realm of our knowledge comprises a clearly bounded set of these instances. The frontiers of science produce the boundary between the known and the unknown which is undoubtedly fractal and we have no grounds to assume it rectifiable or measurable. It is worth noting in parentheses that rather smooth are the routes to the frontiers of science which are charted by teachers, professors, and all other kinds of educationalists. Pedagogics dislikes saltations and sharp changes of the prevailing paradigm. Possibly, these topological obstructions reflect some objective difficulties in modernizing education. The proofs are uncountable of the fractality of the boundary between the known and the unbeknown. Among them we see such negative trends as the unleashed growth of pseudoscience, mysticism, and other forms of obscurantism which creep into all lacunas of the unbeknown. As revelations of fractality appear the most unexpected, beautiful, and stunning interrelations between seemingly distant areas and directions of science. Mathematics serves as the principal catalyst of the unity of science.
We are granted the blissful world that has the indisputable property of unicity. The solitude of reality was perceived by our ancestors as the ultimate proof of unicity. Mathematics has never liberated itself from the tethers of experimentation. The reason is not the simple fact that we still complete proofs by declaring “obvious.” Alive and rather popular are the views of mathematics as a toolkit for natural sciences. These stances may be expressed by the slogan “mathematics is experimental theoretical physics.” Not less popular is the dual claim “theoretical physics is experimental mathematics.” The coupled mottoes reflect the close affinity of the trails of thought in mathematics and natural sciences.
It is worth observing that the dogmata of faith and the principles of theology are also well reflected in the history of mathematical theories. Variational calculus was invented in search of better understanding of the principles of mechanics, resting on the religious views of the universal beauty and harmony of the act of creation.
Mathematics is a rather specific area of intellectual creativity which possess its own unparallel particularities. Georg Cantor, the founder of set theory, wrote in one of his classical papers in 1883 as follows: “…das Wesen der Mathematik liegt gerade in ihrer Freiheit.” In other words, “the essence of mathematics resides in its freedom.” The freedom of modern mathematics does not reduce to the absence of exogenous limitations of the objects and methods of research. To a great extent, the freedom of mathematics is disclosed in the new intellectual tools it provides for taming the universe and liberating a human being by expanding the boundaries of his or her independence.
The twentiethth century marked an important twist in the content of mathematics. Mathematical ideas imbued the humanitarian sphere and, primarily, politics, sociology, and economics. Social events are principally volatile and possess a high degree of uncertainty. Economic processes utilize a wide range of the admissible ways of production, organization, and management. The nature of nonunicity in economics transpires: The genuine interests of human beings cannot fail to be contradictory. The unique solution is an oxymoron in any nontrivial problem of economics which refers to the distribution of goods between a few agents. It is not by chance that the social sciences and instances of humanitarian mentality invoke the numerous hypotheses of the best organization of production and consumption, the most just and equitable social structure, the codices of rational behavior and moral conduct, etc.
The twentieth century became the age of freedom. Plurality and unicity were confronted as collectivism and individualism. Many particular phenomena of life and culture reflect their distinction. The dissolution of monarchism and tyranny were accompanied by the rise of parliamentarism and democracy. Quantum mechanics and Heisenberg’s uncertainty incorporated plurality in physics. The waves of modernism in poetry and artistry should be also listed. Mankind had changed all valleys of residence and dream.
The thesis of universal mathematization enlightened all events of the early history of the Siberian Division. These years are decorated with the outstanding advances in economic cybernetics, theoretical programming, mathematical linguistics, mathematical chemistry, mathematical biology, and many other new synthetical areas of research. Mathematization of the human sciences and the human dimension of the natural sciences become typical of the scientific life in Siberia.
Mathematics is a human science involving the abstractions in which the human beings perceive forms and relations. Mathematics is impossible without the disciples, professional mathematicians. Obviously, the essence of mathematics is disclosed to us only as expressed in the contributions of scientists. Therefore, it would be not a great exaggeration to paraphrase the words of Cantor and say that the essence of a mathematician resides and reveals itself in his or her freedom.
The founding fathers of the Siberian Division, M. A. Lavrentiev, S. L. Sobolev, and S. A. Kristianovich, were renowned mathematicians and mechanicians who carried a great impetus of scientific freedom.
It was the Institute of Mathematical with the Computing Center that became the citadel of mathematical research in Siberia. There were only 7 persons on the staff in 1957, but in a five years the staff of the Institute had listed 520 members.
The Institute of Mathematics, named after his founder and first director S. L. Sobolev, is an eminent mathematical center. There are a few top-class scientific schools in the Institute which are connected with the names of the masters of the first call: Academicians S. L. Sobolev, A. I. Maltsev, L. V. Kantorovich, and A. D. Alexandrov. The present generation of leaders comprises Academicians A. A. Borovkov, S. K. Godunov, Yu. L. Ershov, M. M. Lavrent'ev, and Yu. G. Reshetnyak.
The Sobolev Institute of Mathematics carries out fundamental research in the areas of algebra and logic, geometry and topology, function theory and functional analysis, differential equations and mathematical physics, probability and mathematical statistics, as well as , cybernetics and mathematical economics.
In the fiftieth year of the Siberian Division the belief seems reasonable in the successful proliferation of the academic traditions in mathematics.
April 23, 2007
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