Whereas mathematics proceeds by deductive inference, science characteristically proceeds by inference to the best explanation. The particular kind of inference that characterizes a truth-seeking pursuit is why a distinction between math and science is important.
If two explanatia for the same explanandum are equally probable then, by virtue of lex parsimoniae, the less ontologically superfluous of the two is the better explanation. An example can help to illustrate how science differs from math in that it infers to the best explanation rather than deduces.
Lightning is more/less likely in places with higher/lower atmospheric convection than others yet, regardless of whether or not Zeus makes any lightning at all, it is most likely that there is lightning today if Zeus makes lightning whenever he is mad and if Zeus is mad today. Yet, it is implausible that "Zeus makes lightning whenever he is mad and he is mad today" truly explains that there is lightning today, because it is highly improbable that Zeus is mad today (regardless of how likely it would be that that there is lightning today if Zeus makes lightning whenever he is mad and if he is mad today).
A no less plausible explanation for the lightning today (than an argumentum ad Jove) is that today's lightning was the making of unintelligent natural phenomena, which is plausible because it probably is a fact due to it being true a posteriori on many prior known occasions (whereas "Zeus makes lightning whenever he is mad and he is mad today" is not and has never been known a posteriori).
Moreover, "unintelligent natural phenomena" makes for a better explanation than an argumentum ad Jove because, by virtue of Ockham's Razor, although Zeus might make lightning daily by increasing atmospheric convection daily, to include Zeus in an explanation (of how a natural phenomena caused the lightning today) is unnecessary to explain, sufficiently, today's lightning, which necessarily requires some mention of natural phenomena but does not necessarily require any mention of Zeus. It would be excessive to appeal to Zeus; argumentum ad Jove is not as ontologically parsimonious.
On the topic of the social sciences, I think it's a mistake to think that the social sciences, in general, employ methodology inferior to that employed in natural sciences. Evolutionary biology, historically, has borrowed heavily from economics. "The ultimate subject matter of biology and economics is
one, viz., the life process" (Daly 1968).
Toward the end of the Enlightenment-era, economics began to find a place for itself in the life sciences. Carolus Linnaeus described all life as an 'economy of nature' (Linnæo 1749) and Erasmus Darwin had written of an 'economy of vegetation' (E. Darwin 1791). Post-Enlightenment, the Linnaean imagery was adopted by Charles Robert Darwin, a grandson of Erasmus Darwin, who went so far as to employ the Malthusian population principle from classical political economics (see Malthus 1798) as the architecture for designing his theory of natural selection (see C. Darwin 1860). "Darwin has interested us in the history of nature's technology, i.e., in the formation of the organs [that] serve as instruments of production for sustaining life" (Marx 1887). Ronald A. Fisher, a protégé of political economist Leonard Darwin (who was a son of Charles R. Darwin), unified the Darwinian bioevolutionary theory of natural selection with the Mendelian genetics and, in doing so, he had employed a plethora economics concepts (see Fisher 1930). Fisher even considered the inheriting of household wealth by offspring from their parents to be an extension of a more generalized inheritance process stemming from the inheriting of genes by the offspring from the parents, which is a notion that foreshadowed the Dawkinsian theory of the extended phenotype (see Dawkins 1978). "In organisms of all kinds the young are launched upon their careers endowed with a certain amount of biological capital derived from their parents" (Fisher 1930). The adoption of economics by the life scientists had an influence on economists as well. The application of economics to the life sciences, in turn, resulted in a strong influence from the life sciences on economic theory (e.g. evolutionary and behavioral economics). In fact, Alfred Marshall considered economics to be "biology broadly interpreted" (Marshall 1922). With the influx of physics into the life sciences, recently culminating with the noteworthy work by Jeremy England (2013), it is only reasonable that the torch of progress in economic thought now has been passed on to econophysics.