The mathematics of history makes its analysis since the beginning of the so called historical era: Iran�s culture, between the Caspian Sea and the Persian Gulf (5000 years B.C.), the Sumerian, the Chaldean in the Mediterranean Coast, the Egyptian, the Greco-Roman, the Roman-Gothic (Western), with its creative zone between the Ebro river (Spain) and the mouth of the Rhine river (France, Belgium and Holland); that of India, China, Japan; that of the Nordic Countries and, the Slavic culture, the pre-Columbian cultures: the Mayan and Inca, as well as the process in the Columbian era with the United States of America up to the process of the Hispanic-Portuguese-American countries.� The mathematical law of history is applied, showing itself as the creative force of the great nations it moved in Europe and adjacent areas, originating the Persian, Carthaginian, Roman, Macedonian, Visigoth, French and Teutonic Empires in the first cycle. The Turkish, Spanish, French, English and German ones in the second historical cycle, in chronological order. � In the area of the Slavic Nations, they are ending the first cycle of 1,700 years by the year 2000 and begin the phase of Great Demographic Fractionation. Continental China or People�s Republic of China develop the last nucleus of Unification starting in the year 1950, in its second cycle of 1700 years. Japan is at its highest phase, developing its first nucleus of Unification of the first cycle of 1700 years. In the Americas it moves from North to South: The United States of America, the North of South America: the Great Colombia of the XXI Century, Brazil and the area of Rio de la Plata.� ����� The mathematics of history is not the historical determinism that we already know.� Bolivarian thought was in use and will be in use in the time and in the space of mathematics.� In the Spanish American section of the November, 1970 issue of the European magazine SP, there is an article by the name: �Bol�var: Witness 70� that says in part: �However, and as Ernesto Jim�nez Caballero states, this process of integration, the Liberator�s dream, would have been forged even without Spain. On the one hand, the liberal bourgeoisie proceeding from the revolutions of 1776 in North America and 1789 in France, would succeed in having a United Nations and an Organization of American States.� Bol�var, in his conception, would have united NATO and the Common Market at a Hispanic American scale, under one sole agreement�. �If the proposal made by Bol�var for the creation of a block of political ideology was important, the creation of an economic community was just as important�. �... it is debated in the formation of economic blocks: ALALO, the Andean Pact, the Central American Common Market, geared towards achieving, as much as possible, economic independence from the powerful North Continental Nation�.