I will present some general remarks and some personal opinions and findings (with a constant concern for accuracy and objectivity) about the attempts at mathematizing History , historical events , processes and phenomena.
My many readings (see my various book pages and the books I have read) and my analysis of History made me realize that important historical events and phenomena are (highly) periodic , and that exact correspondences(or similarities or homologies , one of these terms could be chosen ,used and defined) can be found between historical events separated by definite periods of time .
The history of humanity can be considered as the result of the interactions between the lives and actions of human beings moving and acting in time. All humans have a role to play in the unfolding of historical events , but great men (and women) and great thinkers/scientists/reformers constitute the main group of humans who change and drive historical phenomena and happenings across cultures , nations and empires.
Evolution and progress take place in human history , such as technological/scientific progress, the increase in the global human population over millennia and the increase in the surface of political entities from city-states to nation-states and to bigger entities ,etc , but there are also general principles and definite periodicities and regularities in world history. Among these regularities are the stages or phases through which pass most great powers and empires as they rise/fall and go up and down in time. Certain essential periodicities or cycles in history are accompanied by a change or transmutation in values(” moral” , behavioral , sexual, etc).
Relevant concepts can be defined such as the notion of bi-millenary (exact) correspondence and of bi-millenary periodical return of historical events .I will explain and clarify these concepts more when I have time in future writings.
Some philosophical and religious theories talk about eternal return/recurrence and cyclical time (the notion of eternal return constantly permeates the philosophy of Nietzsche) ,but these notions are not defined in a precise or scientific way.
I think that Mathematics and the scientific method , i.e observing phenomena and collecting data,creating hypotheses with the adequate mathematical model, experimental/empirical verification of these hypotheses and building coherent theories, can be used in and applied to human history, provided that this is done in the proper and correct way. Historical chronology plays an important role, and the chronology of events before the Common or Christian era should be somewhat revised and corrected.
Another prerequisite for the impartial and objective study of history is to abandon preconceived ideas and to have a global perspective of human history , avoiding euro-centrism , afro-centrism and all kinds of ethnocentrisms , and avoiding to get stuck in certain habits such as classifying people and cultures into Western and non-Western. One should take into account the fact that geopolitical groupings and alliances change with the passing of time , centuries and decades.
A new discipline called Cliodynamics was created in the last decade . It is an area of research using mathematical , quantitative approaches and modelings to explain historical processes and societies .The practitioners of this discipline have made some interesting observations about historical events and have tried to formulate mathematically backed theories to interpret historical facts , however I think they have not found or discovered the right , convenient , correct and/or precise way to mathematize History and historical phenomena .
If the right mathematical theory of human history can be elaborated, using the scientific method and testing hypotheses in history could be equivalent to and lead to the (precise) prediction of important events taking place in the future of humankind.