The term �decisive battles� is a very broad concept. It must be determined if they are decisive in a war between empires, nations in conquest, or liberty of a continent or geographical areas, that make up large or medium spaces. The battles in the 1st or 2nd period of Great Victories are, in their majority, decisive in the conquest of an empire or nation.� Also in the phase of great depression, whether to occupy or to expel the enemy. Likewise in the military disaster, if it is one sole battle or the last one, if they are various from one or another part of the adversaries. In the phase of decadence or disintegration, the first battle that is fought indicates the beginning of the phase, and the last one, marks the end of the empire. Lastly, in the phase of relative independence, the last one is the decisive battle to begin the phase and that provides liberty to the country. Man is the expression of the historical phase, battles are historical events that express said phase and they form the whole of the nation�s process. Everything is continuity in time and in space. Everything is decisive in the thread of the historical process. In the field of Operational Strategy battles would be defined by the three Clausewitz rules: �The concentration of effort, the strong man�s actions and the decision for the battle in the principal theater of operations�. In the area of National Strategy, High or Grand Strategy, its definition is given with precision, the mathematical-historical concept, the mathematical-historical principle and the mathematics of history, as has been exposed and analyzed in this modest work.� In the mathematical-historical concept, we could say that it is a mathematical and humanistic world, in which the first determines the general process of cultures and civilization, of the creations, development and duration of empires and nations, where man is the expression of historical phases. Man can change his destiny only by mental and spiritual excellence. Evolutions and revolutions follow each other without improvisation or delay, nothing is the work of chance.� In cultures, civilizations and processes of man�s life in the planet, historical happenings and events occur as a chain reaction, as a great gear of a perfect machine, and an operation having a continuity and permanence in time and space.� Everything is exactly fulfilled with an admirable precision.� The process of a mathematical world framed within a humanistic field, of a man who oscillates from a maximum civilization to a minimum one.