This unity of science as descriptive remains, for example, in the time of Thomas Hobbes who argued that deductive reasoning from axioms created a scientific framework, and hence his Leviathan was a scientific description of a political commonwealth. What would happen within decades of his work was a revolution in what constituted "science", particularly the work of Newton in physics. Newton, by revolutionizing what was then called "natural philosophy", changed the basic framework by which individuals understood what was "scientific".
While he was merely the archetype of an accelerating trend, the important distinction is that for Newton the mathematical flowed from a presumed reality independent of the observer, and working by its own rules. For philosophers of the same period, mathematical expression of philsophical ideals was taken to be symbolic of natural human relationships as well: the same laws moved physical and spiritual reality. For examples see Blaise Pascal, Gottfried Leibniz and Johannes Kepler, each of whom took mathematical examples as models for human behavior directly. In Pascal's case the famous wager, for Leibniz, the invention of binary computation and for Kepler the intervention of angels to guide the planets.
In the realm of other disciplines, this created a pressure to express ideas in the form of mathematical relationships. Such relationships, called "Laws" after the usage of the time (see philosophy of science) became the model which other disciplines would emmulate.
August Comte (1797-1857) argued that ideas pass through three rising stages, Theological, Philosophical and Scientific. He defined the difference as the first being rooted in assumption, the second in critical thinking, and the third in positive observation. This framework, still rejected by many, encapsulates the thinking which was to push economic study from being a descriptive to a mathematically based discipline. Karl Marx was one of the first writers to claim that his methods of research represented a scientific view of history in this model.
With the late 19th century, attempts to apply equations to statements about human behavior became increasingly common. Among the first were the "Laws" of philology, which attempted to map the change overtime of sounds in a language.
It was with the work of Darwin that the descriptive version of social theory received another shock. Biology had, seemingly, resisted a basis as a mathematical study, and yet the Theory of Natural Selection and the implied idea of Genetic inheritance - later found to have been ennunciated by Mendel, seemed to point in the direction of a scientific biology based, like physics and chemistry, on mathematical relationships.
With the early 20th century, a wave of change came to science that saw "statistical" study sufficiently mathematical to be "science". This application of statistics to physics would yield Quantum Dynamics and an increasingly statistical view of biology.
The first thinkers to attempt to combine inquiry of the type they saw in Darwin with exploration of human relationships, which, evolutionary theory implied would be based on selective forces, were Freud in Austria and William James in the United States. Freud's theory of the functioning of the mind, and James' work on experimental psychology would have enormous impact on those that followed. Freud, in particular, created a framework which would appeal not only to those studying psychology, but artists and writers as well.
One of the most persuasive advocates for the view of scientific treatment of philosophy would be John Dewey (1859-1952). He began, as Marx did, in an attempt to weld Hegelian idealism and logic to experimental science, for example in his "Psychology" of 1887. However, it is when he abandoned Hegelian constructs, and joined the movement in America called Pragmatism, possibly under the influence of William James' "Principles of Psychology" that he began to formulate his basic doctrine, ennunciated in essays such as "The Influence of Darwin on Philosophy" (1910).
This idea, base on his theory of how organisms respond, states that there are three phases to the process of inquiry:
Problematic Situation, where the typical response is inadequeate.
Isolation of Data or subject matter.
Reflective, which is tested empirically.
With the rise of the idea of quantative measurement in the physical sciences, for example Lord Rutherford's famous maxim that any knowledge that one cannot measure numerically "is a poor sort of knowledge", the stage was set for the conception of the humanities as being precursors to "social science" was set.
This change was not, and is not, without its detractors, both inside of academia and outside. The range of critiques begin from those who believe that the physical sciences are qualitatively different from social sciences, through those who do not believe in statistical science of any kind, through those who disagree with the methodology and kinds of conclusion of social science, to those who believe the entire framework of scientificizing these disciplines is solely, or mostly, from a desire for prestige and to alienate the public.
The rise of industrialism had created a series of social, economic, and political problems, particularly in managing supply and demand in their political economy, the management of resources for military and developmental use, the creation of mass education systems to train individuals in symbolic reasoning and problems in managing the effeects of industrialization itself. The perceived senselessness of the "Great War" as it was then called, of 1914-1918, now called World War I, based in what were perceived to be "emotional" and "irrational" decisions - provided an immediate impetues for a more "scientific" and easier to manage form of decision making. Simply put, to manage the new multi-national enterprises, private and governmental, required more data. More data required a means of reducing it to information upon which to make decisions. Numbers and charts could be interpretted more quickly and moved more efficiently than long texts.
In the 1930's this new model of managing decision making became cemented with The New Deal in the US, and in Europe with the increasing need to manage industrial production and governmental affairs. Institutions such as The New School for Social Research, International Institute of Social History and departments of "social research" at prestigious universities was meant to fill the growing demand for individuals who could quantify human interactions and produce models for decision making on this basis.
Coupled with this pragmatic need, was the belief that the clarity and simplicity of mathematical expression avoided systematic errors of holistic thinking and logic rooted in traditional argument. This trend, part of the larger movement known as Modernism provided the rhetorical edge for the expansion of social sciences.