What do mathematicians think about economics?

Why would a mathematician care about economics at all?

Economics offers mathematicians a recognizable kind of problem: production functions, equilibrium models, and optimization principles that can be stated and studied formally [1]. A course given to mathematics students in 1971 framed the subject this way, aiming its notes at both mathematicians and economists rather than treating economics as a foreign discipline [1]. That framing suggests the appeal is structural: economics poses questions about how systems settle into equilibrium or how resources get allocated, which are the kind of questions formal methods are built to handle.

The historical record shows this isn't a one-way borrowing. A 1935 Moscow conference brought together mathematicians including John von Neumann, Leonid Kantorovich, and Albert W. Tucker, and the exchanges there fed into the formal frameworks that later shaped mathematical economics [3]. The paper argues that this single event linking several research communities mattered for how those frameworks developed and spread, contributing to the intellectual landscape in which postwar mathematical economics could emerge [3]. In other words, mathematicians weren't just applying ready-made tools to an existing field; their interactions helped create the field's formal vocabulary.

The suspicion that math has been used to dress up market claims

A more critical strand holds that mathematics has been partly misused in mainstream economics to justify "unregulated markets" [2]. This is a claim about how models get used, not about whether math belongs in economics at all. The proposed response, which its author calls Critical Mathematical Economics, has two parts: analyze and critique the mathematical models used in mainstream economics, such as the Dynamic Stochastic General Equilibrium models in macroeconomics and the Sonnenschein-Mantel-Debreu theorems, and then improve and extend heterodox models using ingredients from modern mathematics and computer science [2].

The second part is where the constructive work happens. The paper points to methods from non-linear dynamics as used in Post-Keynesian macroeconomics, and discusses (pseudo-) Goodwin cycles along with possible micro- and mesofoundations [2]. It also calls for collaboration between mathematicians and heterodox economists, and for what the author calls Progressive Data Science, with attention to ecological data [2]. The underlying view is that the problem isn't too much mathematics but the wrong mathematics, or mathematics applied without enough scrutiny of its foundations.

Foundations, and the problem of teaching economists' math to mathematicians

Some mathematicians approach economics through the foundations of the mathematics itself. One line of work considers Bishop's constructive mathematics and what that perspective implies for key economic theorems, including results treated as the "crown jewels" of mathematical economics [4]. This is a different kind of skepticism from the critique of mainstream models: it asks whether the existence claims at the heart of economic theory hold up under a stricter standard of what counts as a valid proof. The paper frames this within the broader issue of constructivist mathematics [4].

There is also a practical, pedagogical complaint. A 1981 text aimed at mathematicians noted that books titled "Mathematical economics" or similar had been disappointing, devoting considerable space to expounding standard mathematics rather than to the economics [5]. That is a mathematician's frustration in miniature: the subject is interesting, but the available introductions spend too long on material the reader already knows. The same author's book set out to introduce core economic concepts to students with a mathematical background [5], which implies the gap is real enough to need filling.

So do mathematicians agree about economics?

Not really, and the disagreement is instructive. The historical account argues for a deeper analysis of why mathematicians were motivated to apply their tools to economics in the first place, and for a more nuanced narrative linking those motivations to the social and political contexts of economic modeling [3]. That is a call to treat the mathematician's relationship to economics as something worth explaining, not something obvious. The critical program, by contrast, takes a clear stance: mainstream models have been used to justify a political conclusion, and better mathematics plus heterodox collaboration is the remedy [2].

What ties these together is a shared seriousness about the formal side. Whether the conclusion is that economics needs its foundations rebuilt [4], that its mainstream models need critique and replacement [2], or simply that mathematicians deserve a better introduction to the subject [5], none of these positions treats economics as beneath mathematical attention. The recurring theme is that the mathematics in economics is consequential, and therefore worth getting right.

Sources used in this answer

Related research questions