Clausewitz:

He believed that "War is nothing but the continuation of policy with other means." He defines the general characteristics of war in the social and political world and further identifies the elements that are always present as danger, physical and mental effort, psychological factors and the many impediments to carrying out one’s intentions. War can be of two kinds: that either the objective is to ‘overthrow the enemy’ to render him politically helpless or militarily impotent (forcing him to sign agreements); or "merely to occupy some of his frontier-districts" so that we can annex them or use for bargaining at the peace negotiations. He also describes the trinity of war as violence, chance and politics which he further articulates the concepts as friction and genius. He was also the first to recognize the psychology of the soldier, commander and their respective society essential to the theory of war. In waging war (strategy), he later believed that political leadership should ultimately control and direct the conduct of war, that the political purpose for which a war would be fought should determine the means that are employed. In addition, the force should be suitable and proportionate to the military objective in the political purpose.

Mahan:

Mahan’s view was relatively simplistic and narrow in its focus consigning success to the control and domination, or lack of it, of the sea through "sea power." He believed that only through command of the high and coastal seas by naval domination, or lack of it, would determine the outcome of conflict. His position is defined as command of the sea and control of maritime commerce (to include overseas possessions and access to markets) that would produce national wealth and greatness. He believed that "the stoppage of commerce compels peace" that wars will be won by the economic strangulation of the enemy from the sea. Mahan believed that the primary mission (strategy) of the battle fleet was to engage the enemy’s fleet, to destroy the enemy’s organized force, and to establish one's own control of the seas. He, like Jomini, felt that the strategy had to be employed offensively and concentrated to defeat a foe at a weaker point. Mahan states that there are six general conditions affecting sea power, which he determined were universal and timeless. These are geographical position, physical confirmation, extent of territory, number of population, national character, and the character and policy of governments.

Corbett’s view was that war was an application of force to the attainment of political means. He felt that strategy is the art of directing force to the ends in view. He further divided strategy into two subcategories of major (dealing with ulterior objects or the plan of war) and minor (dealing with the primary objects or the operations of war). He also determined that war and strategy could be either offensive or defensive in nature depending on the circumstance. He discusses and defines limited and unlimited war and how it is a determinant in the planning and operation of war. He also places emphasis on the friction created by a country’s political, diplomatic, commercial and financial positions ("deflection of strategy by politics") as being vital factors in every strategic problem. He relegates naval strategy to controlling/influencing passage and communication acknowledging the difficulty of dominating the seas, as they cannot be physically occupied like land. Corbett defines the function of the fleet as the furtherance or hindrance of military operations ashore, protection or destruction of commerce and prevention or securing of alliances.

Clausewitz and Corbett approach war as a complex totality, always threatening to escape control and more dynamic, but incapable of being set to rules. More of an art than a science.

Jomini and Mahan saw war largely as bringing superior force to bear on an enemy where they were both weaker and subject to decisive loss. They expressed the belief that waging war was a science subject to fixed and definable rules.

Jomini and Clausewitz viewed the enemy’s army as the primary strategic objective of military operations.

Mahan believed that only through command of the high and coastal seas by naval domination, or lack of it, would determine the outcome of conflict.

Corbett believed a combination of both sea and land forces were necessary to achieve political ends.

Jomini was the only one that believed that a government should choose its ablest military commander, then leave him free to wage war according to scientific principles.

Jomini: Strategy is the key to warfare where strategy is controlled by "certain and fixed principles, which are by their nature invariable" scientific principles. These basic principles prescribe only offensive action where you mass forces against a weaker enemy force at some decisive point if strategy is to lead to victory.

Clausewitz: Viewed war as extremely complex and that theory could only illuminate this complexity. He also describes the trinity of war as violence, chance and politics which he furthers articulates the concepts as friction and genius.

Mahan: Like Jomini, Mahan was driven to search for certain unchangeable fundamental truths of warfare, which would remain constant and had universal application. He believed that only through command of the seas by naval domination, or lack of it, would determine the outcome of conflict.

Corbett: He believed that war was an application of force to the attainment of political means. He felt that strategy is the art of directing force to the ends in view.

Art is based on how to think about war and strategy. War is a complex totality, always dynamic threatening to escape control and incapable of being set to rules. Strategy was more of a result of the study of war and the eventual theorizing based on this review, but still subject to the complexities of politics, personalities and national will.

Science teaches you what to think about war through a more rigid and disciplined set of principles and rules. Any hostile action should incorporate these rules and they are not permitted to significantly diverge from the established concepts. Politics and other external dynamics are ignored. The only aspect of warfare susceptible to scientific analysis is strategy.

Science is a critical piece of modern warfare in view of the fact that technology is in a continuous state of flux and the next battle may in fact be conducted through a stateless form (information warfare). The art of waging war requires the analysis of historical warfare and potential aspects of future war. Clausewitz in his work, and Corbett in an indirect manner in his, didn’t believe that a rigid set of concepts and principles could be derived from the study of war. Their approaches emphasize a moving away from the scientifically based effort to quantify and describe war because this prevents the ability to create and craft strategy based on the conditions. Jomini and Mahan firmly adhered to the belief that the scientific nature of war and strategy could be captured and quantified.

Both approaches are important in warfighting because science will drive the strategy and the strategy needs to be creative and flexible enough to indulge the artistic form of waging war. The Clausewitz and Corbett approaches are better suited for study and execution as they permit the creativity and flexibility to assimilate the development of new and better weaponry/technology that affects the science of war. Although science is critical to the discharge of war, the art of war must also be well thought-out, as it will compel the strategy throughout the state of affairs.

The art of war is more relevant and thus more important given that the key to victory in the future will be flexibility and the ability to adapt to advances and hostile state of affairs. Both approaches have merit and are useful, but science will always be the catalyst for altering strategy which will hopefully evolve to address the resiliency required in today’s warfare. In contrast, strict adherence to scientific theory without maintaining flexibility in the face of change and not adapting to the amorphous nature of war will institute failure (Viet Nam, Kosovo). Personally, I favor the wider reaching theories of Corbett and his acknowledgement of the roles of politics and logistics in war as well as the recognition of war as being able to be waged in a limited or unlimited manner.