A Creative Philosophy for Mathematical Economics: Identity, Purpose, and Interdisciplinarity

The podcast explores the complex and fluid identity of mathematical economics, arguing it's not merely a technical tool but a language for representation and understanding. Ali Khan, drawing on his extensive career at Johns Hopkins, emphasizes that the field constantly balances the importation of mathematical techniques with substantive economic questions. He posits that mathematics, like language or art, involves inherent ambiguities and the necessity of exclusion and focus, leading to a "second-order theorizing" about what is included or excluded in economic models.

Khan distinguishes between prediction (forecasting, statistics) and understanding, asserting that mathematical economics primarily serves the latter by providing frameworks for representation. He highlights the historical evolution from 19th-century foundations (Cournot, Walras) to the modern period (1950s) and the Econometric Society's initial aim to formalize economics. A crucial nuance is the role of mathematics as a "servant" to economics versus mathematicians using economic problems to pursue mathematical structures, leading to a constant "tilting" of the subject's identity. He also discusses the formalization of concepts like "economic negligibility" through non-standard analysis, offering an alternative perspective on Edgeworth's conjecture.

The speaker advocates for a pluralistic, open-ended approach to mathematical economics, rejecting dogmatic fundamentalism. He shares his personal journey of embracing interdisciplinarity, moving beyond the confines of the economics department to engage with intellectual history, philosophy (Wittgenstein), anthropology, and history of art. This broader engagement, he believes, enriches mathematical economics by fostering a deeper understanding of expression and human sciences. He implicitly recommends young scholars resist the commodification of research and maintain their agency, pursuing intellectual curiosity over the pressures of top journals and careerism.

Ultimately, Khan critiques the negative effects of the Nobel Prize and top-tier journals, which he argues have created "havoc" by fostering a culture of commodification and pressure that stifles genuine scholarship. He connects this to Francis Ferguson's ideas on labeling and commodification. The discussion extends to the broader human sciences, noting the increasing use of mathematics in political science and sociology, and underscores the inherent interdisciplinarity of institutions like Johns Hopkins. The episode champions a view of mathematical economics as a creative, reflective endeavor that invites deep thought about its own methods and assumptions, rather than a mere instrument for prediction or a game played with abstract symbols.

"mathematics is a language that's the way gibbs stated it and samuelson writes there is a redundancy the article is redundant and mathematics is language"

"to the extent that mathematics is language it is not a recipe it is it has all the slippages and the ambiguities of language"

"it is almost in that sense akin to a photograph or a painting or a novel because it must have and i am now already slipping from mathematics into theorizing it must exclude and it must focus and include what it includes and what it excludes can also be theorized"

"prediction is forecasting it is statistics but understanding but to understand you have to you have to represent"

"the fact that the welfare theorems don't hold in an infinite in a setting with an infinite number of commodities is the final nail in the coffin of capitalism"

"this pluralistic open-ended lack of closure aspect to the subject has come this is there's no room for fundamentalist dogmatic things"

"abraham robinson said no they are like complex numbers"

"the hws conjecture is saying greed is group rational provided you as an economic agent are economically negligible"

"a nobel prize has done havoc for the subject and then these top five journals in the top ten"

"if you read francis ferguson's chapter on bentham in her book on pornography the theory pornography the theory she talks of the importance of labeling to sell something you must have a label it must be commodified and research must be commodified we must be commodified"

"you guys are not interested in economics you are interested in playing games with mathematics"

"there was something you painted for the market and something you painted for yourself"