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How Economics Became a Mathematical Science (Science and Cultural Theory)

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E. Roy Weintraub investigates the relationship between the development of mathematics and economics. He argues that by ignoring that mathematics too is a changing field, historians of economic thought have missed important distinctions. In clarifying the strange relationship between Marshall and mathematical methods in economics he shows how this distinctions give new, important insights. He traces the story of the mathematician Griffith C. Evans and his attempt to do mathematical economics like physics with quantifyable data (influenced by Volterra). In his next chapter he looks at Hilberts influence in mathematics, which is distinct from his impact on metamathematics. Having set the stage for abstract formalisms, he investigates how Gerard Debreu has brought the views of Nicolas Bourbaki, a important abstractionist movement, into economics.
The following two chapters aim to clarify the differences between mathematical and economic culture. As an illustration, he gives a account of a unfruitful correspondence between Don Patinkin and the eccentric mathematician, Cecil Phipps, who also was influencial in the puplication of the famous existence proof of Arrow and Debreu.
After this, Weintraub get's personal and tells the story of his economist father and mathematician uncle and how economics become a topic for well trained mathematicians. Weintraub also tells his own story of a economist turned mathematician as a example of a large inflow of mathematicians into economics.
The last chapter is dedicated to methodological issues.

Dr. Weintraub possesses an understanding of the progression of economic thought--and the sciences in general for that matter--that is incredibly sophisticated and, simultaneously, surprisingly accessible. Weintraub illustrates the importance of CONTEXT--each chapter masterfully contextualizes the concepts of mathematics and economics in living history as they were perceived by the protagonists, reminding us that meanings and objectives change, get tangled with each other, cause myriad misunderstandings and misinterpretations, but also inspire the creation of novel methods. It becomes clear that overly linear and logically atomized constructions of the sciences lead to spurious problems and unanswerable questions (wait until you meet Debreau).

Marshall's nineteenth-century mathematics is practically inseparable from its numerous physical applications, and he gradually becomes out of touch with the field as the Hilbertian axiomatization program takes form and math becomes its OWN (ideally) pristine entity. A stubborn mathematics professor from the University of Florida tries desperately to reject the Arrow-Debreau paper because he badly misinterprets certain economic assumptions. Weintraub's subjects are woven effortlessly throughout and through each episode. We ultimately arrive at Weintraub's personal narrative and watch as the massive moves in economics hit home and affect the professional lives of his father, uncle, and years later, the author himself--creating another stimulating and rich narrative layer for the reader to consider.

A basic history usually provides two dimensions, a linear progression of A begetting B begetting C. A better history considers complex, multi-directional factors that zip around in three dimensions colliding, reinforcing, negating, colluding. Weintraub's account, alas, gives us the rare privilege of four dimensions.

Provocative, unique, sophisticated, and accessible, I recommend this work to anybody remotely curious about the history of economic thought.

I do not know who Michael Brady is, nor what his difficulties are. His comments on this book however are bizarre. Not one element of his "note" is connected to anything I wrote in this book, which is a history, not a presentation of Keynes. He seems to have a personal interpretation of Keynes, sort of like a personal relationship with God, and it seems to lead him to think anyone else cares, or is presenting counter-interpretations. This is wild stuff. Read the book for yourself, or any of the more than a dozen published reviews in several languages, or the award citations from the History of Economics Society or The Society for the History of Economics (each of which presented this book with its best book award), to check my veracity.

The fundamental problem with E Roy Weintraub's book is his a priori belief,reflected in the title,that economics is already a mathematical science.Economics is currently in the same class as administration,accounting,management,finance,marketing,communications,law or urban/regional studies.It is a field,study ,discipline or profession.It is not a science or an art, except in the hands of someone like John Maynard Keynes,Joseph A Schumpeter or Paul Samuelson.The recognition of this fact explains why Alfred Nobel forbade the awarding of any Nobel prize to any economist.It explains why Leon Walras's attempts to be awarded either the Nobel Prize in Literature or Peace were unanimously rejected.The reader of this review should also realize that the Nobel Memorial Prize in Economic Science is not a Nobel Prize.The only winner of this prize who could also be legitimately awarded a Nobel Prize is Paul Samuelson. It is a simple matter to demonstrate that economics is not presently a mathematical science,unless Weintraub's study refers to the fact that economists spend all their time trying to reinterpret, and apply in an ad hoc fashion to economics ,the original mathematical analysis of physicists,chemists,biologists and engineers.Consider the case of the differential calculus analysis presented by Keynes in the General Theory(GT).Keynes's analysis of his D-Z model is presented on pp.55-56,ft.2,pp.280-286,pp.304-306,and on pp.271-278,although this latter analysis would require that the reader of the GT already be familiar with A C Pigou's model as contained in Part II of The Theory of Unemployment(1933)in chapters 8-10.Keynes's analysis of his Y-multiplier model is contained on pp.114-117,126,and p.209 of the GT.Any reader of this review who has taken and presumably passed a lower division course in the first semester of calculus and analytic geometry can obtain Keynes's original models simply by integrating (taking the anti derivative of)Keynes's differential analysis as listed on the pages mentioned above.This has not been done by a single economist since the publication of the GT in 1936.Instead,there has been a 68 year period of"What did Keynes mean?"articles and books.Both E Roy Weintraub and his father,Sydney Weintraub,have contributed to some of the thousands of books,articles, book reviews and contributions to books that never answer the question .The question is never answered because the economists appear to have forgotten how to integrate Keynes's derivatives.For example,it is obvious that Keynes's expected aggregate supply function,Z,can't possibly be equal to pO,as claimed by ,for instance,E Roy Weintraub and Paul Davidson,where p equals an actual price and O equals real output.Simple integration of Keynes's derivatives on either pp.55-56,ft.2 or pp.283-285 reveals that Z must be equal to P+wN,where P is equal to expected economic profit,w is a constant short run money wage,and N is total employment.A simple reading of chapter 20 reveals that Keynes's expected aggregate demand function is D=pO,WHERE p IS AN EXPECTED PRICE,not an actual price.Keynes's D=Z locus makes perfect sense.Unfortunately,this simple result has not been obtained by economists,because economics is not a mathematical science.One can,of course, hope that economics may evolve sufficiently in the future so as to move in the direction of becoming a mathematical science.