Why Turning Economics Into Math Fails

Important knowledge is lost during the translation of economics into mathematics.

Mathematics is often heralded as the ultimate tool for achieving clarity in economics. The idea is that through precise mathematical expressions, we can communicate more effectively, leaving little room for ambiguity or misinterpretation. However, upon closer inspection, this assumption proves to be deeply flawed, especially when applied to the praxeological insights at the heart of economics.

While clarity is certainly important, we must first ask: clarity of what? When we speak of human action in economics, what we seek to clarify are praxeological meanings—insights into the fundamental nature of human behavior under various conditions. These insights are not inherently quantitative or mechanical, yet mathematics demands that we translate them into a formal and mechanical numerical language. This process, far from offering clarity, can often obscure the very essence of the phenomena we are trying to describe.

Mathematics as a Metaphorical Leap

Mathematics, in itself, is a system of formal, quantitative meanings. It expresses relationships between numbers and variables but does not directly speak to the qualitative, human aspects of action. To make mathematical expressions correspond to praxeological insights, we must engage in a kind of metaphorical leap, imagining how the formal relationships between quantities reflect the subjective and qualitative realities of human choice and behavior. This leap requires interpretation and intuition, and far from making things clearer, it often introduces further complexity. The mathematical symbols do not "speak for themselves"—they must be interpreted in light of the human phenomena they attempt to describe, and this interpretation is neither straightforward nor universally agreed upon.

Consider, for example, the ongoing debates around national income identities in modern monetary theory (MMT). These identities are expressed mathematically, yet the precise meaning of these equations—particularly the causality they imply—is far from obvious. Different economists draw radically different conclusions from the same mathematical expressions, demonstrating that mathematics can cloud understanding just as easily as it can clarify it.

Mathematics is often seen as a tool for clarity and precision in economics, but it can just as easily become a source of confusion and manipulation. While models and analyses aim to simplify complex human behavior, they can obscure reality through selective variables, biased assumptions, or overly rigid frameworks. In such cases, mathematics shifts from a tool of discovery to one of persuasion, where the apparent rigor of numbers masks the subjective decisions behind them.

Statistics, especially, is vulnerable to this kind of rhetorical manipulation. By adjusting sample sizes, selecting specific data ranges, or cherry-picking variables, economists can craft narratives that support nearly any conclusion. The veneer of objectivity that math provides often hides these subjective choices, creating the illusion of certainty. This can lead not to clearer understanding, but to deeper confusion, as the complexity of real economic phenomena is reduced to artificial constructs that may distort more than they reveal. Thus, while math is intended to clarify, it can instead obscure the very realities it seeks to explain.

Furthermore, to make praxeological insights fit into mathematical expressions, we must often invent fictitious quantities. Take, for instance, the utility function, which attempts to represent the praxeological insight that human beings act to remove felt uneasiness. In order to formalize this insight, economists introduce the notion of "utility" as a measurable quantity. But utility, like uneasiness, does not exist as a real, quantifiable variable. Uneasiness is a category of subjective experience – the removal of which is the motivation to act and inarticulable in precise terms. Yet mathematics demands that we reduce uneasiness and other categories of action into numbers. This reduction introduces a layer of fiction—we are no longer dealing with action but with further symbolic representations that may or may not correspond to action.

One danger is that once these mathematical variables are created, they take on a life of their own. Economists begin manipulating them within equations, deriving results that may have nothing to do with the underlying praxeological reality. The formalism obscures the original meaning rather than clarifying it. For example, despite widespread agreement that utility is an ordinal, not cardinal, concept, many economists continue to treat it as if its cardinality is meaningful, leading to conclusions that distort the original praxeological insight.

Precision, Clarity, and the Role of Tacit Knowledge

Precision does not necessarily lead to clarity. Mathematics, by its very nature, requires us to introduce certain elements in order for statements to be valid within its formal system. But these elements are often artificial, and the process of making praxeological insights "fit" into mathematical formalisms can distort or obscure their true meaning. As a result, what is mathematically precise may not be praxeologically clear. In fact, there are many instances where it is clearer to be “vague and imprecise”—where the imprecision of natural language allows us to express meanings that cannot be captured by the strict rules of formal systems.

The term "I" in natural language might seem vague when viewed through the lens of mathematics, but this “vagueness” is not a flaw—it's an inherent feature of how we communicate complex and deep realities. The difficulty in defining "I" arises not from the absence of understanding, but from the nature of how we understand it: much of what constitutes "I" is tacit knowledge—knowledge that we hold but may not be able to articulate. As Michael Polanyi explains, our awareness of the particulars that make up this knowledge is subsidiary—they remain in the background, shaping our understanding of the whole without being directly in focus.

When we attempt to dissect "I" into its particular components (when we try to formalize it and be “precise”), we encounter the issue of focal ignorance. Our understanding of "I" is grounded in an implicit, holistic grasp that cannot be easily broken into particulars like personal history, body, or soul. When we try to identify one these particulars, we realize we can’t, yet they still function as a part of the whole. This unarticulated knowledge continues to operate beneath the surface, guiding our understanding despite our inability to express it explicitly.

The problem becomes more complicated. By focusing on these particulars, we can run into an issue that causes us to lose sight of the whole. This phenomenon, as Polanyi describes, occurs because the particulars—elements we tacitly understand—cannot be explicitly defined without disrupting our broader comprehension. For example, consider a pianist in mid-performance: if they begin concentrating on the physics of each individual movement of their fingers, the overall coherence and flow of the music would break down. The issue isn’t a lack of knowledge; rather, it is that the pianist’s tacit knowledge, which underpins their performance, is being forced into explicit focus, where it cannot function as it should. This disruption of the tacit-to-explicit balance exemplifies why breaking down the "I" into articulable parts distorts rather than clarifies our understanding.

This principle extends beyond personal identity and into economics. Just as the meaning of "I" resists formal articulation, many praxeological insights—the fundamental truths about human action and it as a whole—are grasped tacitly and resist reduction to rigid mathematical terms without distorting their meaning. When we attempt to formalize praxeology into precise mathematical models, we face the same issue as when trying to define "I" in exact terms. Praxeological categories, like uneasiness, which drives human action, are tacitly understood. Uneasiness cannot be fully captured in numbers or equations, but mathematics demands we 1) articulate the inarticulable 2) reduce such complex experiences to variables and functions—artificial symbols that may bear little resemblance to the actual phenomena. This reduction introduces a layer of fiction, confusing symbolic representations for reality and distorting the true nature of human action, just as trying to quantify "I" would obscure the richness of personal identity.

Furthermore, mathematics itself requires a significant degree of tacit understanding—from interpreting symbols to intuiting the relationships between variables—which adds even more complexity. This means that when we mathematize economics, we not only distort the praxeological insights, but we also layer on additional requirements of tacit knowledge. 1) about mathematics 2) about human action 3) understanding the relationship of the math to human action. The addition of the fictional layer of math compounds the difficulty of grasping the reality of economic phenomena.

Conclusion

Polanyi’s critique of this formalization process is not just about the limitations of mathematics in expressing complex realities; it strikes at the heart of a deeper issue: the belief that knowledge must be objective, impersonal, and fully articulated to be valid. He argues that all knowledge is personal, rooted in the tacit dimension of understanding, where particulars are integrated into a whole without explicit articulation. Tacit knowledge is the foundation of all knowledge. This personal participation in knowledge is not a flaw but an essential feature of how we comprehend the world. Even in the most formal systems of knowledge, such as mathematics or logic, the understanding and application of those systems depend on tacit knowledge. The symbols we manipulate on a page are meaningless without the person interpreting and understanding them.

In this way, the mathematical formalization of economics represents a flawed pursuit of knowledge. It attempts to strip away the personal, tacit dimension, as if knowledge could exist independently of the knower, like some objective "pellet" of truth waiting to be discovered. But this is a false ideal. As Polanyi shows, even the most precise knowledge relies on the tacit integration of particulars—an integration that cannot be formalized without distorting the whole. This is why praxeological insights, and many other truths about human action, are often better expressed in vague, qualitative terms rather than in the rigid, quantified language of mathematics. It allows us to understand the meaning of the whole. In stripping away “vagueness”, we may also strip away meaning.