Notes on Too Much Math and Too Little History in Economics

Overview

• Proposition: there is too much math and too little history in economics as it’s currently taught and conceived.
• The talk frames two complementary paths to understanding economies: mathematics (rigor, proofs) and history (context, reality checks), which are argued to sit at opposite poles in terms of epistemology.
• The speakers debate whether economics should emphasize mathematical modeling or historical understanding, with calls for a pluralist, “horses for courses” approach.

Math in economics: what it tries to do

• Math has two aims, according to the speaker:
  • Propositions that are necessarily true; a branch of logic.
  • Propositions that can be proved; mathematics as generating provable results.
• Economists generally endorse math for the second aim (proofs), but the social system is so complex that reliable proofs are often not obtainable.
• The “Platonic temptation”: economists are tempted to view math as the path to rigorous, elegant laws, akin to celestial mechanics.
• Krugman’s critique (cited after the 2008-2009 crash):
  • "The economics profession went astray because economists, as a group, mistook beauty clad in impressive sounding mathematics for truth. Economists fell in love with the old idealized vision of an economy in which rational individuals interact in perfect markets, this time gussied up with fancy mathematics. It's an old vision gussied up with fancy math." $ext{(Krugman, after the 2008-09 crisis)}$
• The drift toward Platonism helps explain the strong normative thrust of mathematical economics: models are viewed as real, and the world should resemble the model rather than the model resembling the real world.
• A model is an assumed simplification; an assumption is chosen for its purchase on reality, but often it is chosen for mathematical convenience (to solve an equation, exclude extraneous elements).
• Exclusionism: modeling choices define which problems are deemed important and which viewpoints are excluded; this shapes inquiry and policy implications.
• Because of the inherent difficulty of proving anything in complex social systems, mathematical economics can push the real world to fit the model rather than the model fitting the real world.

History as reality check

• The role of history is to provide a reality check against theoretical propositions.
• Propositions like “risks are correctly priced on average” often fail when confronted with actual financial markets or economic history.
• Historical branches that are particularly relevant but often minimized in standard curricula:
  • Economic history
  • History of economic thought
  • Political and social history
• History is excluded or minimized in many curricula due to the belief that everything history offers is already captured in the latest textbooks.
• Physics envy: economists sometimes treat economics as a hard science and assume history’s lessons are embedded in modern models, making historical study seem unnecessary.
• J.B. Say on studying past errors (Say’s Law context):
  • "What useful purpose can be served by the study of absurd opinions and doctrines that have long since been exploded and deserve to be forgotten? It is mere useless pedantry to attempt to revive them. The more perfect a science becomes, the shorter becomes its history. Our duty with regard to errors is not to revive them but simply to forget them." $ext{(Say)}$
• Contemporary curricula often reflect Say’s dictum, neglecting past mistakes and debates in economic thought.
• The study of the history of economic thought reveals that important debates (e.g., the quantity theory of money, state spending efficiency) remain unresolved and are inherited by current schools (neoclassical, post-Keynesian, etc.).
• History shows that economic ideas depend on context; the same proposition can have different validity depending on circumstances (e.g., Great Depression era, post-1970s inflation).

Debates about context, method, and truth

• Examples used to illustrate the context-sensitivity of economic ideas:
  • Keynesian Revolution arose from the Great Depression.
  • Friedman’s monetarism emerged in response to inflation in the 1970s.
  • The marginalist revolution in the 1870s can be seen as an attempt to refute Marx’s labor theory of value; the idea that factors of production are paid their marginal products highlighted the value of business input to society.
• Robert Solow’s perspective on history and econometrics:
  • Economic activity is embedded in a web of social institutions, beliefs, and attitudes.
  • Time-series data, if long enough, tend to be noisy; the longer the series, the harder it is to discriminate among hypotheses, and the more stubborn the results can appear. As data length grows, the likelihood of discarding hypotheses declines and the noise grows; cleverness and persistence can yield almost any result.
• The history of economic thought also shows how financial theory often serves the interests of powerful groups (e.g., banking sector) in shaping regulatory outcomes.
• The claim that economic truth is context-dependent argues against universal, timeless theories; rather, theories should adapt to changing conditions.

The practical stance: pluralism and “horses for courses”

• The argument for a pluralist approach: economics benefits from multiple methodologies (math, econometrics, surveys, historiography, etc.)
• The idea is not to abolish math but to use division of labor: some people do math, some do econometrics, others do history and surveys.
• The famous Adam Smith reference: division of labor is the origin of economics; proponents argue that it is appropriate to have different specialists for different problems.
• Development economics often requires relatively little math because the main issues concern governance and institutions; in contrast, forecasting supply and demand for a specific product or sector heavily relies on math.
• Therefore, there is a case for mathematical microeconomics but a concern that history has been banished from curricula, leading to reduced pluralism and greater arrogance in the discipline.
• The cost-benefit perspective: weigh the benefits gained from math against the costs in terms of time and cognitive load for students; a reasonable use of math should reflect its practical payoff.

Counterpoints from the pro–history side and responses

• Some critics claim economics today is empirically driven and empiricism—not math obsession—driven by data and observation; math is not the sole driver of research.
• The use of the term “frictions” is criticized as importing a physics/engineering mindset; the language and assumptions may bias theory toward physics-inspired models rather than social realities.
• The advocates for math concede a division of labor: not everyone should, or can, master every method; some should focus on math, others on econometrics, history, and qualitative methods.
• The cost of over-mathematization is the risk of arrogance and reduced openness to alternative approaches; thus, a balanced program is necessary.

Final synthesis and recommendations

• The speakers emphasize that progress in economics is not necessarily from moving from specific to general via math; economics does not follow the same path as natural sciences.
• A call for pluralism: embrace multiple methodologies and contexts; avoid the dogma that one approach is universally superior.
• Practical governance: tailor the methodological toolkit to the problem at hand (e.g., use math where precise forecasting is essential; rely on history and qualitative analysis where governance and institutions dominate).
• Acknowledgement that math has a vital role, especially in forecasting and microeconomic analysis, but history, including economic thought history, is essential to avoid hubris and to maintain relevance to real-world change.

Notable quotes and references mentioned

• Paul Krugman (post-2008 crisis):
  • "The economics profession went astray because economists, as a group, mistook beauty clad in impressive sounding mathematics for truth. Economists fell in love with the old idealized vision of an economy in which rational individuals interact in perfect markets, this time gussied up with fancy mathematics. It's an old vision gussied up with fancy math."
• J.B. Say on the value of studying historical errors:
  • "What useful purpose can be served by the study of absurd opinions and doctrines that have long since been exploded and deserve to be forgotten? It is mere useless pedantry to attempt to revive them. The more perfect a science becomes, the shorter becomes its history. Our duty with regard to errors is not to revive them but simply to forget them."
• John Stuart Mill’s recognition (1844) of pre-mathematical insights, used to critique the notion that math alone capitalizes on economics.
• Adam Smith on division of labor as the origin of economics.
• Robert Solow on the embedding of economic activity in social institutions and the limits of long historical time series for discriminating hypotheses.
• The shift from insular to pluralist approaches is framed as a defense against intellectual arrogance and a pathway to more useful economics.

Notable historical anchors and dates mentioned

• Crash of $2008-2009$ as a turning point for the critique of overly mathematical models.
• The $Great Depression$ as the historical backdrop for Keynesian revolution.
• The $1970s$ inflation as the catalyst for Friedman’s monetarism.
• The $1870s$ marginalist revolution as a response in part to Marx’s labor theory of value.
• The year $1844$ associated with Mill and Say in discussions of economic thought.

Closing sentiment

• Acknowledgement that empirically driven economics exists, but the discipline should remain open to multiple methodologies and viewpoints.
• The evening ends with a call for a more humble, pluralistic, and practically oriented economics that uses history as a reality check and math as a tool, not a sole guide.