In 1989, Hubert M. Blalock Jr. wrote in the American Sociological Review that "Sociology is not a high-quality discipline." Sociology students score at the bottom on standardised tests — not only in quantitative reasoning, but in verbal reasoning. Between 1950 and 2010, the proportion of quantitative articles in Britain's leading sociology journals fell from 32% to 16%, while qualitative research rose from 8% to 43%. Over 60% of sociology students prefer writing essays to analysing data. This is not mere method preference. It reflects a disciplinary culture in which the rejection of mathematical training is an open secret.

The common defence for avoiding formalisation holds that social phenomena are instantaneous and local — formalized language cannot capture a world of meaning constructed through subjective human interpretation. David Bloor's Strong Programme pushes further: even mathematical truths are social constructs, making their application to a fluid social world epistemologically suspect. This critique has deep institutional roots; by the 1960s, an anti-quantitative culture was systematically built into the expanding university system. But equating mathematical modelling with the pursuit of "eternal truth" is itself a narrow view. As Ravetz argued, models are metaphors — their value lies in facilitating dialogue and clarifying assumptions, not in perfectly representing reality.

A sharper question is needed: Is it that mathematics cannot yet accurately describe social facts — or is it that sociologists' mathematical proficiency has not reached the point where they could use it to do so? Economics offers a reference: from Cournot to Arrow–Debreu, mathematical formalisation was contested but maintained its ambition. Mathematical sociology, by contrast, has largely failed — not because the project is impossible, but because mathematical sociologists themselves misunderstood the role models should play: treating them as tools for empirical generalisation rather than as creative instruments for theory construction. The gap is not in mathematics itself. It is cognitive: the distance between existing formal tools and sociology's core concerns around meaning, context, and historicity.

Quantitative sociology is far more than regression. A useful distinction includes at least five types: statistical models (regression, SEM, multilevel, causal inference); network models (centrality, ERGMs, community detection); dynamical systems (differential equations, opinion dynamics, cultural diffusion — once prominent in mathematical sociology, now nearly absent); discrete and logical models (rational choice, axiomatic theory); and computational models (ABM, machine learning). Contemporary quantitative sociology is dangerously concentrated on statistical models alone. When causal inference becomes the only legitimate goal, regression becomes the only legitimate tool — and the model toolkit impoverishes itself. Blalock's insight was that the value of mathematical modelling extends far beyond causal estimation; its fundamental function is to clarify concepts and locate troublesome issues in theory.

Sensitivity Analysis and Sensitivity Auditing — as developed by Saltelli and Puy — provide operational tools for quantitative self-reflection. SA systematically varies inputs and assumptions to assess which factors drive conclusions. SAUD extends the audit to the full modelling process: what interests, blind spots, and value presuppositions are embedded? The core claim: the quality of numbers requires technical rigour and normative transparency. Applied to sociology — does a regression's core coefficient survive changes in control variables? Does a network model embed the assumption that denser ties are better? Does an ABM's behavioural rule implicitly assume a specific conception of rationality? These questions force quantitative research out of the black box and into a broader community of scrutiny.

A reflexive quantitative sociology requires three capacities simultaneously: solid mathematical and statistical training that extends beyond regression to differential equations, graph theory, and game theory; keen theoretical intuition to judge what is worth quantifying and what is not; and a clear awareness that even the most "objective" quantitative methods embed specific value presuppositions and cognitive frameworks. This reflexivity may be the bridge between positivist and interpretive sociology. As Harrison White once said: "I cannot imagine achieving what we want without mathematics at all. But the mathematics we need may not be the mathematics we currently have." The inadequacy of existing tools is not a reason to abandon formalisation — it is an invitation to explore new mathematical languages capable of capturing fluidity and complexity. The real danger is not using mathematics, but abusing it: letting methods dominate questions, and letting technique replace thought.