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Harmony Forum

Peace from Harmony
First International Congress on Mathematics of Harmony: Odessa, Ukraine, October 8-10, 2010

First International Congress o­n Mathematics of Harmony:

Odessa, October 8-10, 2010




Congress Initiator:

Prof. Alexei Stakhov (Canada)


Honorary member, Global Harmony Association (GHA)

Member, GHA Board and General Directorate of GHA World Harmony Academy 



Author of the cornerstone book "The Mathematics of Harmony" (2009),
which is the foundation of mathematics of harmonious civilization



Personal page:

In English: http://peacefromharmony.org/?cat=en_c&key=330

In Russian: http://peacefromharmony.org/?cat=ru_c&key=350


Congress o­n Mathematics of Harmony, Odessa, October 8-10,2010
In Russian: http://peacefromharmony.org/?cat=ru_c&key=471
In English: http://peacefromharmony.org/?cat=en_c&key=441



Harmonious Civilization Culture

Citizens of Earth!

Unite in harmony for peace, justice, fraternity and happiness!


Global Harmony Association (GHA)

Since 2005, GHA is an international NGO uniting more 400 members in 48 countries and more than o­ne million participants from the GHA collective members in 80 countries. GHA Founder and President is Dr. Leo Semashko, Russia.

GHA-USA President is Dr. Laj Utreja.

GHA-Japan President is Kae Morii.

Web: www.peacefromharmony.org

GHA Mission: to peace from harmony; Or: pave the conscious way for harmonious civilization



From Alexei Stakhov’s Mathematics of Harmony

To Mathematics of Four-dimensional Spheral Fractals of

Harmonious Civilization

GHA Call to Mathematicians of the World


The modern history is an unprecedented tectonic shift of human civilization/noosphere from the outgoing industrial o­ne to the nascent harmonious o­ne. Its seismic tremors are felt at all levels of spiritual culture. The spontaneous flow of collective cultivation of a harmonious global civilization streams worldwide.

In 2009, the GHA witnessed the global harmonious civilization birth with the appearance of its first three attributes:

1. Beginning of nuclear disarmament of the USA and Russia in 2009, which is impossible in militaristic industrial civilization,

2. Appearance of its first theoretical model in 2009 (GHA book "Harmonious Civilization": http://www.peacefromharmony.org/?cat=en_c&key=379), and

3. Mathematics of Harmony as the arithmetic of a new civilization: Prof. Alexei Stakhov, Canada in 2009 (http://www.worldscibooks.com/mathematics/ 635.html).

The first economic proof of this civilization is an unprecedented philanthropy of the 40 U.S. billionaires overturning industrialism. Its social proofs are the EU from 1992 and China from 2006, both building a harmonious society in their territories with a collective population of about 2 billion: it is almost a third of mankind.

Mathematics has always been an essential tool for the practical realization of human knowledge, which, as known, becomes a science o­nly through mathematics. Harmonious civilization from the beginning, with first-year, becomes the object of a fundamentally new quality (socially) and mathematical thinking. The first occurs in the form of the harmony alphabet as a list of 20 of its fundamental elements/spheres, and the second appears in the form of its arithmetic as Alexey Stakhov’s mathematics of harmony.

Its importance for a new civilization is like to Euclid’s "Geometry Elements". It reveals the fundamental role of harmonious, "golden" proportions in the nature, society and human. It is elementary mathematics (arithmetic) of world harmony. It is the basis for subsequent mathematics of harmonious civilization. As Tetrasociology laid the foundations of social science of that civilization as and harmony mathematics laid the foundations for its mathematical science. Tetrasociology unfolds o­n a qualitative level the fractal nature of society and its harmony through the hierarchical structure of self-similar matrix sphere indicators of resources, processes, structures and spheral classes of the population. The basic matrix of spheral statistics of PIOT resources (people, information, organization, things) by the dimension of 4 x 4 has the form:

P1 + P2 + P3 + P4

I1 + I2 + I3 + I4

О1 + О2 + О3 + О4

T1 + T2 + T3 + T4

The system of these matrices is defined by the formula: 4 x 4 to the power K, where K is a row of natural numbers. (For more detail see book: Harmonious Civilization, 2009, pp 210-213: http://peacefromharmony.org/?cat=en_c&key=400).

Mathematics of harmonious civilization will evolve from two-dimensionality of arithmetic to multidimensional algebra of harmony. GHA has identified the next stage of development of mathematics of harmonious civilization o­n the path of synthesis of the four-dimensional matrixes of Semashko’s spheral indices of Tetrasociology, Stakhov’s harmony arithmetic and Mandelbrot’s mathematical theory of fractals. The matrixes of the spheral statistics, mathematical definition of harmonious proportions and balance of which allow to create a full scientific picture of social harmony in the dynamic and at any level (global, regional, national and local) are special, social, fractals, to which the fractals theory spreads.

Therefore, the task of development of mathematics of harmonious civilization, from our point of view, reduced to solving the task of harmonious proportions of the spheral social fractals. Of course, the GHA does not exclude the possibility of refinement for this key mathematical problem of harmonious civilization.

In June 2010 the GHA addressed with a letter (http://peacefromharmony.org/?cat=ru_c&key=461) to the famous mathematician Gregory Perelman in an open letter to solve the problem of harmonious proportions of the spheral social fractals. Its solution is a key scientific resource for conscious building a harmonious civilization in all the follow-human history and at all levels.

Having received no response from Perelman, we address this call to mathematicians around the world, especially to the participants of the first International Congress, Odessa, October 8-10, 2010, devoted to Stakhov’s mathematics of harmony.


Alexey Stakhov in the letter to Leo Semashko of 9 December 2010

"Dear Leo!
I admire your remarkable report of the Odessa Congress, and your wonderful photos evoke the pleasant memories of Odessa. And of course I thank you for appreciating my scientific direction. "

Leo Semashko


Report o­n the First International Congress o­n Mathematics of Harmony



In Russian: http://peacefromharmony.org/?cat=ru_c&key=471



First International Congress o­n Mathematics of Harmony was initiated by Prof Alexei Stakhov, the creator of Harmony Mathematics and a member of the Global Harmony Association (GHA) Board. It was hold in the Odessa University, October 8-10, 2010.

The GHA emphasizes the primary organizational role and merit of Odessa National University in holding this outstanding mathematical Congress. For great contribution to its organization the GHA expresses hearty thanks to past rector - Valentin Smyntyna, the present Rector - Ivan Koval, to whom we gave our book "Harmonious Civilization" (another its copy - in the University library), Director, IMEMO Victor Kruglov, Head of Department Eugenia Sadchikova and Associate Professor, Tatiana Yegorova-Gudkova, o­n whose shoulders lay all the direct institutional care of Congress. Congress has been provided by these organizers very good! Thank you very much!

Because to this Congress is devoted a new big website: https://sites.google.com/site/harmonymathkongress/, which is given detailed information about its participants, organizers, papers, resolution, and published more than 100 photos, so my report is o­nly a brief supplement of this site and is limited the participation of the GHA in Congress, my work o­n it, its value for the GHA and 33 of my photos from this Congress.

The historical significance of this Congress can not be overestimated, as it was devoted to mathematics of harmony as o­ne of the cornerstones of a harmonious civilization o­n the threshold of which mankind has entered in 2009. The social value of harmony mathematics and the birth of a new civilization are still poorly understood. But it is well disclosed in the GHA works and, above all, in the GHA special leaflet: "From Alexei Stakhov’s Mathematics of Harmony to Mathematics of Four-dimensional Spheral Fractals of Harmonious Civilization." This leaflet is published above, and it was distributed to the Congress participants. Congress shown a growing number of independent mathematicians and different scientists support, develop and successfully apply (especially impressive is discovery of Dr. Sergei Yakushko of Sumy, who unfolded the golden ratio in the chemical elements of Mendeleyev's periodic system) math of harmony of Alexei Stakhov in various fields.

The Congress was attended (according to the list) about 50 scholars, 6 of whom are members of the GHA: Alex Stakhov, Oleg Bodnar, Ivan Mityay, Eduard Soroko, Ivan Raylyan and Leo Semashko. Although we did not present a unified delegation, but we was united by a clear understanding of the enormous importance of mathematics of harmony and its further development for the formation of a new, harmonious civilization.

My job at this Congress, as well as o­n others (in July I was a member of the World Congress of Sociology in Gothenburg, Sweden), was limited the dissemination of the GHA ideas, books and leaflets, as well as establishing new contacts and attract new members to the GHA. In addition to our leaflet, I brought to Odessa about 20 books of "Harmonious Civilization," which I gave to a few (about 10) university libraries and the most prominent speakers, as a result, contacts were established with more than 20 members of Congress.

My report to the Congress, which is published below (in Russian: http://peacefromharmony.org/?cat=ru_c&key=471), was devoted to the theme: "Harmonious Civilization, Tetranet Thinking and Mathematics of Harmony.” Its main idea was to appeal to the mathematicians to solve the problem/hypothesis of harmonious proportions of the spheral social fractals. In it I see the most socially significant development of mathematics of harmony, and its transition from a binary arithmetic of golden proportions to algebra of tetral social fractals. This "algebra of harmony" will not o­nly keep but also rising to a new level " arithmetic of harmony." The solution of this hypothesis, which is incomparably more important than Poincaré conjecture, will empower to arm each student by the math of harmonious solutions (finding a harmonious proportions) of any social and individual problems posed accordingly. This will be a celebration of harmonious mind and thinking, equipped with math of harmony! That was my main thought in the paper.

In its development and consolidation, I offered to write in the Resolution of Congress the relevant paragraph increasing the golden proportions to the area of a harmonious civilization. He was included in the resolution and read as follows: “14. Support the initiative of the Global Harmony Association (Leo Semashko) to establish within it an international department of “Golden proportions of a harmonious civilization." President of the department has agreed to become Alexey Stakhov and Vice-Presidents: American mathematician, Dr. Scott Olsen and Ukrainian mathematician Dr. Tatyana Yegorov-Gudkov.

Development and arithmetic, and algebra of harmony have great scientific importance for the formation and evolution of a harmonious civilization, so it is o­ne of the most important activities of the GHA, which will be expanded and strengthened in the GHA, in close cooperation with all the structures of the golden section, which are created by Alexey Stakhov.

In connection with the successful holding of the First International Congress o­n Mathematics of harmony and make it officially the world value, GHA offers to recognize Professor Alexey Stakhov, the initiator of the Congress and the mathematics of harmony, in the GHA highest Honorary Title "World Harmony Creator", which is officially proclaimed o­n the Global Harmony Day: June 21, 2011 with the presentation and publication of the o­n the Certificate o­n personal page of Alexei Stakhov.


December 8, 2010


33 photos of the Congress and Odessa:

Aleksey Stakhov and Leo Semashko before the opening of Congress in the Odessa University

Main paper of Alexei Stakhov about mathematics of harmony in Congress

Audience of Congress

Ivan Mitya (Kiev) with the GHA book "Harmonious Civilization

Sergey Yakushko (Sumy) with the GHA leaflet

Scott Olsen (USA) with a paper

Members of Congress

Ivan Raylyan with a paper o­n the Chilean scientist Dario Salas Sommer

Star maestro, fantastic pianist Leonid Timoshenko

Comp - poet Yuri Zimbalist, vocal - Gregory Martynenko (St. Petersburg)

Poet Yuri Zimbalist with a poem dedicated to Alexei Stakhov and mathematics of harmony

Gregory Martynenko with a paper

Cradle (beginning) of Odessa

Odessa port

Beautiful Flowers in Odessa

Portico (colonnade) of Odessa


Perhaps, the destiny will smile in Odessa ....

Alexander Pushkin in background of Vorontsov's Palace

Coastal Boulevard

Best Laocoön in the world

Best Opera in Europe (what a harmony!)

Odessa Opera Children

The thirteenth chair (obviously without the diamonds) in the night Odessa

The next morning, my paper

Award: Alla Vavilov, student, athlete, photographer ....

With the golden section sing like a nightingale: Irina Litovchenko and Tatiana Egorova

Tatyana Egorova: chief conductor of the Congress - with tears of tenderness in its finale

Urban park: the way to the train station

On the Rue de Richelieu

On the Rue de Richelieu Cafe Mozart

On the Rue de Richelieu mansions as in St. Petersburg ...

At the Richelieu end: - Station at St-Petersburg .... Goodbye beautiful, harmonious Odessa ...





Odessa, October 8-10, 2010


Mechnikov’s Odessa National University holds the First International Congress o­n the theme "MODERN ASPECTS OF HARMONY MATHEMATICS AND ITS APPLICATION IN THE ECONOMY, SCIENCE, TECHNOLOGY, SOCIETY, AND EDUCATION on October 8-10, 2010.

The well-known scientists and experts in the field, in particular, Doctor in Engineering A. Stakhov (Canada, Bolton), Doctor in Philosophy E. Soroko (Minsk, Belarus), Doctor in Philosophy A.Voloshinov (Russia, Saratov), Doctor in Philosophy Scott Olsen (USA), Doctor in Fine Arts O. Bodnar (Ukraine, Lvov), Doctor in Physics and Mathematics S. Petoukhov (Russia, Moscow), Doctor in EconomicsI. Kryuchkova (Ukraine, Kiev), Doctor in Engineering S. Bushuev, Doctor in EconomicsV. Bondarenko (Russia, Moscow), Doctor in Philology G. Martynenko (Russia, St. Petersburg), and other scholars will participate in the Congress.

In 2009 the International Publishing House "World Scientific" has published the book "The Mathematics of Harmony. From Euclid to Contemporary Mathematics and Computer Science” by Alexey Stakhov http://www.worldscibooks.com/mathematics/6635.html .

This book is a reflection the "golden" paradigm of ancient Greeks (Pythagorean doctrine about numerical harmony of the universe, Plato’s cosmology) in modern science.The book aroused a great attention of many leading scientists of the world (Prof. Scott Olsen, USA, Prof. Volkmar Weiss, Germany, Prof. Abachiev Sergey, Russia) who are considering the publication of this book as a major event in the history of science.

Mechnikov’s Odessa National University has decided to introduce the course "The Mathematics of Harmony" into the curriculum of training of students specializing in Management of Organizations, 4-th course. Setting and lecturing o­n this course will be made by Prof. Stakhov in September-October 2010.

The Congress has for an object largely informational purpose o­nly. Its main objective is to fix the priority of the Ukrainian science in the development of this important area and to inform participants about the essence of the "Harmony Mathematics" as a new interdisciplinary direction of modern science and the work of the Odessa National University o­n the introduction into the educational process of a new course "Mathematics of Harmony". Therefore, we decided to invite to the Congress's leading experts in this field as Invited Speakers. Theywill make the reports (29 reports) o­n the theory of "Harmony Mathematics and its applications in various fields of modern science at the plenary sessions (8-9 October). The remaining participants will have the opportunity to share their experiences during the "Round Table" (October 10).

By preparing to the Congress, the University already has created "The Museum of Harmony Mathematics", which shows a pictorial history of the Harmony Mathematics, starting with Pythagoras, Plato, Euclid, and the existence of the "Harmony Mathematics" in nature and art in the form of 34 colored posters.

We invite the scientists and professors from Ukraine, Russia and elsewhere to take part in the Congress to obtain new scientific information in the form of reports, books and textbook and then to transfer this information students of universities.



2. PresidiumoftheCongress



V.А. Smintyna

Rector of Mechnikov’s Odessa National University, Doctor in Physics and Mathematics, Professor, Academician

А.P. Stakhov

President of the International Club of the Golden Section, Doctor in Engineering, Professor (Canada)



Soroko E.М.

Doctor in Philosophy, Institute of Philosophy, Byelorussian Academy of Sciences (Belorussia, Minsk)




Doctor in Economics, Deputy Minister of Economy of Ukraine

Bushuev S.D,

President of the Ukrainian Association of Project Management, Head of the Department of Project Management, Kiev National Academy of Construction and Architecture, Doctor in Engineering, Professor

Scott Olsen

PhD in Philosophy, Professor, College of Central Florida (U.S.)

Bodnar O. Ja.

Doctor in Art, Professor, Corresponding Member of the National Academy of Arts of Ukraine, Lviv National Academy of Arts (Ukraine)

Voloshinov А.V.

Doctor in Philosophy, PhD in Physics and Mathematics, Saratov Technical University (Russia)


Doctor in Phylology, Professor, Sant-Petersburg University (Russia)


Doctor in Physics and Mathematics, PhD in Biology, Professor, Engineering Institute, Russian Academy of Sciences (Moscow)

Ivanus А.I.

PhD in Engineering, Trapesnikov’s Institute of Management, Russian Academy of Sciences (Moscow)

Raylyan I.G.

PhD in Engineering, member of Russian Academy of Natural Sciences (Chili)


PhDinBiology, Professor, Vice-rectorofNationalUniversityofLifeandEnvironmentalSciencesofUkraine (Kiev, Ukraine)


PhD in Philosophy, Professor, Institute of Public Administration, Law and innovative technologies (Russia, Moscow).

Congress Organizer:
Mechnikov’s OdessaNational University

Co-organizers of the Congress:
- International Club of the Golden Section, Canada

- Foundation “The Future of the Region", Odessa
The working languages of the Congress:

Ukrainian, Russian, English

Editions of the Congress:

1.Abstracts of invited speakers of the Congress – up to 10 pages.

2.Abstracts of poster presentations - up to 5 pages. Review of abstracts by the working group of the Organizing Committee for compliance with the topics of the Congress.

3.Transcript of the Roundtable

Information o­n the Congress is presented at:

Web-site of Mechnikov’s OdessaNational University - www.onu.edu.ua

Web-sites of the International Club of the Golden Section: www.goldensectionclub.net , goldensectionclub.blogspot.com

Web-site of Institute for Creative Technologies - www.InstituteOfCreativeTechnologies.com

Web-site of Foundation “The Future of the Region" - www.FutureOfRegion.org


Plenary lectures

General Lectures


1.Stakhov A.P., Doctor in Engineering (Canada). The Mathematics of Harmony as a New Paradigm of Modern Science: a Survey of the Main Results

2.Scott Olsen, Doctor in Philosophy (USA). The Golden Section. Nature’s Greatest Secret

3.Soroko E.M., Doctor in Philosophy (Belarus). A Law of Structural Harmony of Systems in the Local Objects of Nature and Society.

4.Voloshinov A.V. , Doctor in Philosophy, PhD in Mathematics(Russia). Structural Harmony of Nature in the Structures of Art

5.Martynenko G. Ja., Doctor in Philology (Russia). Humanitarian Aspects of the Mathematics of Harmony

6.Abachiev S.K. PhD in Philosophy (Russia). The Mathematics of Harmony: difficult historical fate and great prospects

7.Bodnar O.Ja., Doctor in Arts (Ukraine). The Golden Section and Geometry of Nature.

8.Petoukhov S.V., Doctor in Physics and Mathematics (Russia).The Genetic Code, the Golden Section and Musical Structure of the Golden Wurf.

9.Kleschov D.S.(Russia). Solution of the Contradictions in the Axioms of Arithmetic and Constructive Mathematics as a Means of Harmonization of Modern Mathematical Science



10.Kryuchkova I.V., Doctor in Economics (Ukraine). The manifestation of the Law of the Golden Section in the Structuring of Economy.

11.Bondarenko V.M. Doctor in Economics (Russia). Harmony Mathematics of Human Relations: Two Paradigms of Development

12.Bushuev S.D, Doctor in Engineering (Ukraine). Innovative mechanisms of the program for the development of complex systems

13.Sadchenko E.V. (Ukraine). Harmonization as a methodological approach to prevent crises.

14.Yegorova-Gudkova T.I. PhD in Economics (Ukraine). Using the Fundamental Constants of the Harmony Mathematics for Justifying the Invariants of Economical Growth Strategy

15.Ivanus A.I. PhD in Engineering (Russia). Self-harmonization of Competitive Market Systems Based o­n the Generation of New Knowledge

16.Kharitonov A.S., PhD in Physics and Mathematics (Russia). The Golden Section in the Evolution of Systems with Distributed Structure

17.Solovyov V.N. Doctor in Mathematics (Ukraine).Econophysics of crisis phenomena

18.ChechikA.L., ZaikinaE.A. (Украина). Selecting the main criterion and mathematical models to assess the socio-economic development at the macro level.

Botany, Biology, Medicine


19.Tsvetkov V.D. PhD in Biology (Russia). Heart, the Golden Harmony and a Principle of Optimal Entry

20.Mitjay I.S. PhD in Biology (Ukraine). The Golden Section and Wurf as Organizing Principles and Invariants of Natural Systems

21.Burlaku V.Z., Doctor in Medicine,PostolakiA.I. PhD in Medicine (Moldova). A Concept o­n the Regularities of Structural Organization and Morphogenesis of Human Dental System o­n the Basis ofSpiral Bio-symmetry


Mathematics, Fibonacci numbers theory, Engineering


22.Kognovitsky O.S. PhD in Engineering (Russia). Analysis of Recurrent Sequences of the Generalized Fibonacci Numbers by Using the Dual Basis

23.Vladimirov V.L. Doctor in Engineering (Germany).Fibonacci & Lucas Sequences and Golden Mean Degrees as Special Cases of Divisorial Recurrence Sequences

24.Jugannikov A.Ju. PhD, (Russia). The Golden Section and cenoses in technical systems


Spirituality, Morality and the Harmony of Cosmos


25.Raylyan I.G. PhD in Engineering (Chile). Physical Foundations of Morality

26.Morgun E.V.,diakon (Ukraine). The System of Knowledge based o­n the Doctrine of the Christian Philosopher John of Damascus as an Example of Harmonization of the Relationship between Faith and Science

27.Bystrov M.V. (Russia). Our Main Choice of Life: Break-down through the Foundations of Mathematics to the Spiritual.

28.Timoshenko L.V., Composer, Director of the Cultural Centre "Wave of the Future" (Russia).. Golden Proportions of Cosmos Sounding .

29.Tereshina E.V. Doctor in Biology (Russia). A Doctrine o­n Duality and Trinity - the Basis of the Ancient World Picture

30.Semashko L.M. PhD in Philosophy (Russia). Harmonious Civilization and Tetranet-balanced Thinking




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Registration fee can be paid o­n the fact of coming to Congress.

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Details of payment: payment ofregistration fee for the participation in the Congress., Odessa, October 5-10, 2010






To participate in the Congress you must complete the registration form and send it by e-mail. Within o­ne working day,the organizers of the Congress will send you a confirmation of receipt of the application and prepare a contract and an invoice for the provision of services within the Congress.

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